Spall strength - Revision history

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	'''Spall strength''' '''<math>(\sigma_{sp})</math>''' is defined as the maximum [[Stress (mechanics)\|tensile stress]] a material can withstand under dynamic loading conditions before internal failure occurs due to [[spallation]]. Spallation is a high-rate fracture phenomenon in which a material experiences rapid void nucleation, growth, and coalescence due to the release of compressive [[shock waves]] and the subsequent formation of tensile waves. Unlike traditional [[tensile strength]], spall strength is measured under conditions involving [[Shock (mechanics)\|shock]] loading, making it highly [[strain rate]] dependent. The critical importance of spall strength spans across [[high-energy physics]], [[aerospace engineering]], and [[planetary science]], where materials are frequently exposed to extreme dynamic stresses.<ref name=":0">{{Cite book \|date=2003 \|title=Spall Fracture \|url=https://link.springer.com/book/10.1007/b97226 \|language=en \|doi=10.1007/b97226\|bibcode=2003spfr.book.....A \|isbn=0-387-95500-3 \|last1=Antoun \|first1=Tarabay \|last2=Curran \|first2=Donald R. \|last3=Razorenov \|first3=Sergey V. \|last4=Seaman \|first4=Lynn \|last5=Kanel \|first5=Gennady I. \|last6=Utkin \|first6=Alexander V. }}</ref>		'''Spall strength''' '''<math>(\sigma_{sp})</math>''' is defined as the maximum [[Stress (mechanics)\|tensile stress]] a material can withstand under dynamic loading conditions before internal failure occurs due to [[spallation]]. Spallation is a high-rate fracture phenomenon in which a material experiences rapid void nucleation, growth, and coalescence due to the release of compressive [[shock waves]] and the subsequent formation of tensile waves. Unlike traditional [[tensile strength]], spall strength is measured under conditions involving [[Shock (mechanics)\|shock]] loading, making it highly [[strain rate]] dependent. The critical importance of spall strength spans across [[high-energy physics]], [[aerospace engineering]], and [[planetary science]], where materials are frequently exposed to extreme dynamic stresses.<ref name=":0">{{Cite book \|date=2003 \|title=Spall Fracture \|url=https://link.springer.com/book/10.1007/b97226 \|language=en \|doi=10.1007/b97226\|bibcode=2003spfr.book.....A \|isbn=0-387-95500-3 \|last1=Antoun \|first1=Tarabay \|last2=Curran \|first2=Donald R. \|last3=Razorenov \|first3=Sergey V. \|last4=Seaman \|first4=Lynn \|last5=Kanel \|first5=Gennady I. \|last6=Utkin \|first6=Alexander V. }}</ref>

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wikipedia>Daniel Quinlan: Nominated for deletion; see :Wikipedia:Articles for deletion/Spall strength.

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	{{Short description\|Measure for strength of a material}}		{{Short description\|Measure for strength of a material}}

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	'''Spall strength''' '''<math>(\sigma_{sp})</math>''' is defined as the maximum [[Stress (mechanics)\|tensile stress]] a material can withstand under dynamic loading conditions before internal failure occurs due to [[spallation]]. Spallation is a high-rate fracture phenomenon in which a material experiences rapid void nucleation, growth, and coalescence due to the release of compressive [[shock waves]] and the subsequent formation of tensile waves. Unlike traditional [[tensile strength]], spall strength is measured under conditions involving [[Shock (mechanics)\|shock]] loading, making it highly [[strain rate]] dependent. The critical importance of spall strength spans across [[high-energy physics]], [[aerospace engineering]], and [[planetary science]], where materials are frequently exposed to extreme dynamic stresses.<ref name=":0">{{Cite book \|date=2003 \|title=Spall Fracture \|url=https://link.springer.com/book/10.1007/b97226 \|language=en \|doi=10.1007/b97226\|bibcode=2003spfr.book.....A \|isbn=0-387-95500-3 \|last1=Antoun \|first1=Tarabay \|last2=Curran \|first2=Donald R. \|last3=Razorenov \|first3=Sergey V. \|last4=Seaman \|first4=Lynn \|last5=Kanel \|first5=Gennady I. \|last6=Utkin \|first6=Alexander V. }}</ref>		'''Spall strength''' '''<math>(\sigma_{sp})</math>''' is defined as the maximum [[Stress (mechanics)\|tensile stress]] a material can withstand under dynamic loading conditions before internal failure occurs due to [[spallation]]. Spallation is a high-rate fracture phenomenon in which a material experiences rapid void nucleation, growth, and coalescence due to the release of compressive [[shock waves]] and the subsequent formation of tensile waves. Unlike traditional [[tensile strength]], spall strength is measured under conditions involving [[Shock (mechanics)\|shock]] loading, making it highly [[strain rate]] dependent. The critical importance of spall strength spans across [[high-energy physics]], [[aerospace engineering]], and [[planetary science]], where materials are frequently exposed to extreme dynamic stresses.<ref name=":0">{{Cite book \|date=2003 \|title=Spall Fracture \|url=https://link.springer.com/book/10.1007/b97226 \|language=en \|doi=10.1007/b97226\|bibcode=2003spfr.book.....A \|isbn=0-387-95500-3 \|last1=Antoun \|first1=Tarabay \|last2=Curran \|first2=Donald R. \|last3=Razorenov \|first3=Sergey V. \|last4=Seaman \|first4=Lynn \|last5=Kanel \|first5=Gennady I. \|last6=Utkin \|first6=Alexander V. }}</ref>

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	==Representative values==		==Representative values==

	Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979}}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|volume=11 \|issue=3 \|pages=398–410 \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM...11..398F \|issn=2199-7454\|doi-access=free }}</ref>		Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979\|url-access=subscription }}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|volume=11 \|issue=3 \|pages=398–410 \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM...11..398F \|issn=2199-7454\|doi-access=free }}</ref>

	These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.		These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.

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	==Mechanisms==		==Mechanisms==
	Spallation is initiated when a compressive shock wave traverses a solid and releases at a free surface or an interface with a lower impedance material, creating a tensile rarefaction wave. If the tensile stress exceeds the dynamic tensile strength of the material, spallation occurs.<ref name=":0" /> The stress state generated by shock wave release is governed by the [[Rankine–Hugoniot conditions]], which describe conservation of mass, momentum, and energy across shock fronts. For a planar shock:		Spallation is initiated when a compressive shock wave traverses a solid and releases at a [[free surface]] or an interface with a lower impedance material, creating a tensile rarefaction wave. If the tensile stress exceeds the dynamic tensile strength of the material, spallation occurs.<ref name=":0" /> The stress state generated by shock wave release is governed by the [[Rankine–Hugoniot conditions]], which describe conservation of mass, momentum, and energy across shock fronts. For a planar shock:

	<math>P = \rho_0 u_s u_p</math>		<math>P = \rho_0 u_s u_p</math>

wikipedia>Harry reynold: /* growthexperiments-addlink-summary-summary:3|0|0 */

2026-04-26T19:11:18Z

growthexperiments-addlink-summary-summary:3|0|0

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	<math>P = \rho_0 u_s u_p</math>		<math>P = \rho_0 u_s u_p</math>

	where <math>P</math> is the shock pressure, <math>u_s</math> is the shock velocity, and <math>u_p</math> is the particle velocity.<ref name=":0" />		where <math>P</math> is the shock pressure, <math>u_s</math> is the shock velocity, and <math>u_p</math> is the [[particle velocity]].<ref name=":0" />

	Once tensile stress is achieved, [[dislocation]] motion becomes the dominant [[Plasticity (physics)\|plasticity]] mechanism. At very high strain rates (<math>>10^6 \, \text{s}^{-1}</math>), dislocation density increases rapidly, enhancing the material's [[flow stress]] according to:		Once tensile stress is achieved, [[dislocation]] motion becomes the dominant [[Plasticity (physics)\|plasticity]] mechanism. At very high strain rates (<math>>10^6 \, \text{s}^{-1}</math>), dislocation density increases rapidly, enhancing the material's [[flow stress]] according to:
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	</math>		</math>

	where <math>Q</math> is the activation energy for diffusion, <math>R</math> is the [[gas constant]], and <math>T</math> is the absolute temperature.<ref name=":0" />		where <math>Q</math> is the [[activation energy]] for diffusion, <math>R</math> is the [[gas constant]], and <math>T</math> is the absolute temperature.<ref name=":0" />

	Material anisotropy and heterogeneity can significantly influence spall behavior. For example, additively manufactured metals often contain porosity, [[residual stress]]es, and texture that reduce spall strength.<ref>{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Dippo \|first3=O. \|last4=Beal \|first4=R. A. \|last5=Livescu \|first5=V. \|last6=Martinez \|first6=D. T. \|last7=Trujillo \|first7=C. P. \|last8=Florando \|first8=J. N. \|last9=Kumar \|first9=M. \|last10=Gray \|first10=G. T., III \|date=2016-10-04 \|title=Spall fracture in additive manufactured Ti-6Al-4V \|url=https://doi.org/10.1063/1.4963279 \|journal=Journal of Applied Physics \|volume=120 \|issue=13 \|pages=135902 \|doi=10.1063/1.4963279 \|bibcode=2016JAP...120m5902J \|osti=1328489 \|issn=0021-8979}}</ref><ref name=":3" /> [[High-entropy alloys]] and [[amorphous metals]], with their complex microstructures and high defect tolerance, show promise for improved performance under extreme loading.<ref name=":6">{{Cite journal \|last1=Thürmer \|first1=Daniel \|last2=Zhao \|first2=Shiteng \|last3=Deluigi \|first3=Orlando R. \|last4=Stan \|first4=Camelia \|last5=Alhafez \|first5=Iyad Alabd \|last6=Urbassek \|first6=Herbert M. \|last7=Meyers \|first7=Marc A. \|last8=Bringa \|first8=Eduardo M. \|last9=Gunkelmann \|first9=Nina \|date=2022-02-25 \|title=Exceptionally high spallation strength for a high-entropy alloy demonstrated by experiments and simulations \|url=https://www.sciencedirect.com/science/article/pii/S0925838821039773 \|journal=Journal of Alloys and Compounds \|volume=895 \|article-number=162567 \|doi=10.1016/j.jallcom.2021.162567 \|osti=1843121 \|issn=0925-8388}}</ref><ref name=":7">{{Cite journal \|last1=Yuan \|first1=Fuping \|last2=Prakash \|first2=Vikas \|last3=Lewandowski \|first3=John J. \|date=2007-02-01 \|title=Spall strength and Hugoniot elastic limit of a zirconium-based bulk metallic glass under planar shock compression \|url=https://doi.org/10.1557/jmr.2007.0053 \|journal=Journal of Materials Research \|language=en \|volume=22 \|issue=2 \|pages=402–411 \|doi=10.1557/jmr.2007.0053 \|bibcode=2007JMatR..22..402Y \|issn=2044-5326\|url-access=subscription }}</ref> Accurate prediction of spall strength thus requires detailed understanding of both the material’s intrinsic properties and the external loading conditions.		Material anisotropy and heterogeneity can significantly influence spall behavior. For example, additively manufactured metals often contain porosity, [[residual stress]]es, and texture that reduce spall strength.<ref>{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Dippo \|first3=O. \|last4=Beal \|first4=R. A. \|last5=Livescu \|first5=V. \|last6=Martinez \|first6=D. T. \|last7=Trujillo \|first7=C. P. \|last8=Florando \|first8=J. N. \|last9=Kumar \|first9=M. \|last10=Gray \|first10=G. T., III \|date=2016-10-04 \|title=Spall fracture in additive manufactured Ti-6Al-4V \|url=https://doi.org/10.1063/1.4963279 \|journal=Journal of Applied Physics \|volume=120 \|issue=13 \|pages=135902 \|doi=10.1063/1.4963279 \|bibcode=2016JAP...120m5902J \|osti=1328489 \|issn=0021-8979}}</ref><ref name=":3" /> [[High-entropy alloys]] and [[amorphous metals]], with their complex microstructures and high defect tolerance, show promise for improved performance under extreme loading.<ref name=":6">{{Cite journal \|last1=Thürmer \|first1=Daniel \|last2=Zhao \|first2=Shiteng \|last3=Deluigi \|first3=Orlando R. \|last4=Stan \|first4=Camelia \|last5=Alhafez \|first5=Iyad Alabd \|last6=Urbassek \|first6=Herbert M. \|last7=Meyers \|first7=Marc A. \|last8=Bringa \|first8=Eduardo M. \|last9=Gunkelmann \|first9=Nina \|date=2022-02-25 \|title=Exceptionally high spallation strength for a high-entropy alloy demonstrated by experiments and simulations \|url=https://www.sciencedirect.com/science/article/pii/S0925838821039773 \|journal=Journal of Alloys and Compounds \|volume=895 \|article-number=162567 \|doi=10.1016/j.jallcom.2021.162567 \|osti=1843121 \|issn=0925-8388}}</ref><ref name=":7">{{Cite journal \|last1=Yuan \|first1=Fuping \|last2=Prakash \|first2=Vikas \|last3=Lewandowski \|first3=John J. \|date=2007-02-01 \|title=Spall strength and Hugoniot elastic limit of a zirconium-based bulk metallic glass under planar shock compression \|url=https://doi.org/10.1557/jmr.2007.0053 \|journal=Journal of Materials Research \|language=en \|volume=22 \|issue=2 \|pages=402–411 \|doi=10.1557/jmr.2007.0053 \|bibcode=2007JMatR..22..402Y \|issn=2044-5326\|url-access=subscription }}</ref> Accurate prediction of spall strength thus requires detailed understanding of both the material’s intrinsic properties and the external loading conditions.
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	Ongoing research in spall strength is focused on advanced materials and improved characterization techniques. [[Additive manufacturing]] has introduced new challenges and opportunities; researchers aim to understand how layer-wise construction, residual stresses, and porosity influence spall behavior.<ref name=":5" /><ref>{{Cite journal \|last1=Gray \|first1=G. T. \|last2=Livescu \|first2=V. \|last3=Rigg \|first3=P. A. \|last4=Trujillo \|first4=C. P. \|last5=Cady \|first5=C. M. \|last6=Chen \|first6=S. R. \|last7=Carpenter \|first7=J. S. \|last8=Lienert \|first8=T. J. \|last9=Fensin \|first9=S. J. \|date=2017-10-01 \|title=Structure/property (constitutive and spallation response) of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S1359645417306158 \|journal=Acta Materialia \|volume=138 \|pages=140–149 \|doi=10.1016/j.actamat.2017.07.045 \|bibcode=2017AcMat.138..140G \|osti=1463491 \|issn=1359-6454}}</ref> Computational modeling is becoming increasingly multiscale, coupling [[molecular dynamics\|atomistic simulations]] with [[continuum mechanics]] to predict spall initiation and evolution.<ref>{{Cite journal \|last1=Wang \|first1=Xin-Xin \|last2=He \|first2=An-Min \|last3=Zhou \|first3=Ting-Ting \|last4=Wang \|first4=Pei \|date=2021-09-01 \|title=Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation \|url=https://www.sciencedirect.com/science/article/pii/S0167663621002246 \|journal=Mechanics of Materials \|volume=160 \|article-number=103991 \|doi=10.1016/j.mechmat.2021.103991 \|bibcode=2021MechM.16003991W \|issn=0167-6636\|url-access=subscription }}</ref> In-situ diagnostics, such as ultrafast X-ray imaging at [[synchrotrons]] or [[Free-electron laser\|XFELs]], provide real-time observations of void dynamics during spall events.<ref>{{Cite journal \|last1=Wang \|first1=Xiaoming \|last2=Rigg \|first2=Paulo \|last3=Sethian \|first3=John \|last4=Sinclair \|first4=Nicholas \|last5=Weir \|first5=Nicholas \|last6=Williams \|first6=Brendan \|last7=Zhang \|first7=Jun \|last8=Hawreliak \|first8=James \|last9=Toyoda \|first9=Yoshimasa \|last10=Gupta \|first10=Yogendra \|last11=Li \|first11=Yuelin \|last12=Broege \|first12=Douglas \|last13=Bromage \|first13=Jake \|last14=Earley \|first14=Robert \|last15=Guy \|first15=Dale \|date=2019-05-10 \|title=The laser shock station in the dynamic compression sector. I \|url=https://doi.org/10.1063/1.5088367 \|journal=Review of Scientific Instruments \|volume=90 \|issue=5 \|pages=053901 \|doi=10.1063/1.5088367 \|pmid=31153279 \|bibcode=2019RScI...90e3901W \|osti=1542978 \|issn=0034-6748}}</ref><ref>{{Cite journal \|last1=Flanagan \|first1=R. M. \|last2=Fensin \|first2=S. J. \|last3=Meyers \|first3=M. A. \|date=2022-01-19 \|title=The role of pre-existing heterogeneities in materials under shock and spall \|url=https://doi.org/10.1063/5.0053693 \|journal=Applied Physics Reviews \|volume=9 \|issue=1 \|pages=011305 \|doi=10.1063/5.0053693 \|bibcode=2022ApPRv...9a1305F \|osti=1841029 \|issn=1931-9401}}</ref> These experiments are helping to refine constitutive models and damage criteria.		Ongoing research in spall strength is focused on advanced materials and improved characterization techniques. [[Additive manufacturing]] has introduced new challenges and opportunities; researchers aim to understand how layer-wise construction, residual stresses, and porosity influence spall behavior.<ref name=":5" /><ref>{{Cite journal \|last1=Gray \|first1=G. T. \|last2=Livescu \|first2=V. \|last3=Rigg \|first3=P. A. \|last4=Trujillo \|first4=C. P. \|last5=Cady \|first5=C. M. \|last6=Chen \|first6=S. R. \|last7=Carpenter \|first7=J. S. \|last8=Lienert \|first8=T. J. \|last9=Fensin \|first9=S. J. \|date=2017-10-01 \|title=Structure/property (constitutive and spallation response) of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S1359645417306158 \|journal=Acta Materialia \|volume=138 \|pages=140–149 \|doi=10.1016/j.actamat.2017.07.045 \|bibcode=2017AcMat.138..140G \|osti=1463491 \|issn=1359-6454}}</ref> Computational modeling is becoming increasingly multiscale, coupling [[molecular dynamics\|atomistic simulations]] with [[continuum mechanics]] to predict spall initiation and evolution.<ref>{{Cite journal \|last1=Wang \|first1=Xin-Xin \|last2=He \|first2=An-Min \|last3=Zhou \|first3=Ting-Ting \|last4=Wang \|first4=Pei \|date=2021-09-01 \|title=Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation \|url=https://www.sciencedirect.com/science/article/pii/S0167663621002246 \|journal=Mechanics of Materials \|volume=160 \|article-number=103991 \|doi=10.1016/j.mechmat.2021.103991 \|bibcode=2021MechM.16003991W \|issn=0167-6636\|url-access=subscription }}</ref> In-situ diagnostics, such as ultrafast X-ray imaging at [[synchrotrons]] or [[Free-electron laser\|XFELs]], provide real-time observations of void dynamics during spall events.<ref>{{Cite journal \|last1=Wang \|first1=Xiaoming \|last2=Rigg \|first2=Paulo \|last3=Sethian \|first3=John \|last4=Sinclair \|first4=Nicholas \|last5=Weir \|first5=Nicholas \|last6=Williams \|first6=Brendan \|last7=Zhang \|first7=Jun \|last8=Hawreliak \|first8=James \|last9=Toyoda \|first9=Yoshimasa \|last10=Gupta \|first10=Yogendra \|last11=Li \|first11=Yuelin \|last12=Broege \|first12=Douglas \|last13=Bromage \|first13=Jake \|last14=Earley \|first14=Robert \|last15=Guy \|first15=Dale \|date=2019-05-10 \|title=The laser shock station in the dynamic compression sector. I \|url=https://doi.org/10.1063/1.5088367 \|journal=Review of Scientific Instruments \|volume=90 \|issue=5 \|pages=053901 \|doi=10.1063/1.5088367 \|pmid=31153279 \|bibcode=2019RScI...90e3901W \|osti=1542978 \|issn=0034-6748}}</ref><ref>{{Cite journal \|last1=Flanagan \|first1=R. M. \|last2=Fensin \|first2=S. J. \|last3=Meyers \|first3=M. A. \|date=2022-01-19 \|title=The role of pre-existing heterogeneities in materials under shock and spall \|url=https://doi.org/10.1063/5.0053693 \|journal=Applied Physics Reviews \|volume=9 \|issue=1 \|pages=011305 \|doi=10.1063/5.0053693 \|bibcode=2022ApPRv...9a1305F \|osti=1841029 \|issn=1931-9401}}</ref> These experiments are helping to refine constitutive models and damage criteria.

	Researchers are also exploring novel material systems, including high-entropy alloys, [[metallic glasses]], and [[bioinspired composites]], for enhanced dynamic strength.<ref name=":6" /><ref name=":7" /><ref>{{Cite journal \|last1=Wu \|first1=Gang \|last2=Wang \|first2=Xin \|last3=Wang \|first3=Yuting \|last4=Ji \|first4=Chong \|last5=Zhao \|first5=Changxiao \|last6=Gao \|first6=Yuxuan \|date=2023-10-01 \|title=Blast response of bioinspired nacre-like staggered composite plates combined with steel and polyurea \|url=https://www.sciencedirect.com/science/article/pii/S0734743X23002294 \|journal=International Journal of Impact Engineering \|volume=180 \|article-number=104719 \|doi=10.1016/j.ijimpeng.2023.104719 \|bibcode=2023IJIE..18004719W \|issn=0734-743X\|url-access=subscription }}</ref> The integration of [[machine learning]] into material design workflows is being used to predict spall performance across compositional and processing spaces.<ref>{{Cite journal \|last1=Frawley \|first1=Keara G. \|last2=Thadhani \|first2=Naresh N. \|last3=Ramprasad \|first3=Rampi \|last4=Sahu \|first4=Harikrishna \|date=2025-03-12 \|title=A machine learning approach to predicting the spall strength of metals and alloys \|journal=Journal of Applied Physics \|volume=137 \|issue=10 \|pages=104905 \|doi=10.1063/5.0248560 \|bibcode=2025JAP...137j4905F \|issn=0021-8979\|doi-access=free }}</ref> As a result, spall strength research continues to evolve at the intersection of materials science, mechanics, and data-driven engineering.		Researchers are also exploring novel material systems, including high-entropy alloys, [[metallic glasses]], and [[bioinspired composites]], for enhanced dynamic strength.<ref name=":6" /><ref name=":7" /><ref>{{Cite journal \|last1=Wu \|first1=Gang \|last2=Wang \|first2=Xin \|last3=Wang \|first3=Yuting \|last4=Ji \|first4=Chong \|last5=Zhao \|first5=Changxiao \|last6=Gao \|first6=Yuxuan \|date=2023-10-01 \|title=Blast response of bioinspired nacre-like staggered composite plates combined with steel and polyurea \|url=https://www.sciencedirect.com/science/article/pii/S0734743X23002294 \|journal=International Journal of Impact Engineering \|volume=180 \|article-number=104719 \|doi=10.1016/j.ijimpeng.2023.104719 \|bibcode=2023IJIE..18004719W \|issn=0734-743X\|url-access=subscription }}</ref> The integration of [[machine learning]] into material design workflows is being used to predict spall performance across compositional and processing spaces.<ref>{{Cite journal \|last1=Frawley \|first1=Keara G. \|last2=Thadhani \|first2=Naresh N. \|last3=Ramprasad \|first3=Rampi \|last4=Sahu \|first4=Harikrishna \|date=2025-03-12 \|title=A machine learning approach to predicting the spall strength of metals and alloys \|journal=Journal of Applied Physics \|volume=137 \|issue=10 \|pages=104905 \|doi=10.1063/5.0248560 \|bibcode=2025JAP...137j4905F \|issn=0021-8979\|doi-access=free }}</ref> As a result, spall strength research continues to evolve at the intersection of [[materials science]], mechanics, and data-driven engineering.

	== References ==		== References ==

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	==History==		==History==
	The origins of spall strength studies date back to early [[ballistic]] and explosive experiments in the 20th century. Initial documentation of dynamic fracture can be traced to [[Bertram Hopkinson\|Hopkinson’s]] 1914 experiments.<ref>{{Cite journal \|last=Williams \|first=Cyril Labode \|date=2022-10-05 \|title=Void Mediated Failure at the Extremes: Spallation in Magnesium and Aluminum \|journal=Metals \|language=en \|volume=12 \|issue=10 \|pages=1667 \|doi=10.3390/met12101667 \|doi-access=free \|issn=2075-4701}}</ref> During [[World War II]], extensive research at [[Los Alamos National Laboratory]] under the leadership of [[J. Robert Oppenheimer]] and colleagues investigated shock-induced failure in [[nuclear materials]].<ref>{{Cite journal \|last1=Crockett \|first1=Scott D. \|last2=and Freibert \|first2=Franz J. \|date=2021-12-03 \|title=Equation of State: Manhattan Project Developments and Beyond \|url=https://doi.org/10.1080/00295450.2021.1913036 \|journal=Nuclear Technology \|volume=207 \|issue=sup1 \|pages=S286–S294 \|doi=10.1080/00295450.2021.1913036 \|arxiv=2103.05773 \|bibcode=2021NucTe.207S.286C \|issn=0029-5450}}</ref><ref name=":1">{{Cite journal \|last1=Brown \|first1=Eric N. \|last2=and Borovina \|first2=Dan L. \|date=2021-12-03 \|title=The Trinity High-Explosive Implosion System: The Foundation for Precision Explosive Applications \|url=https://doi.org/10.1080/00295450.2021.1913954 \|journal=Nuclear Technology \|volume=207 \|issue=sup1 \|pages=S204–S221 \|doi=10.1080/00295450.2021.1913954 \|arxiv=2103.05714 \|bibcode=2021NucTe.207S.204B \|issn=0029-5450}}</ref> These efforts laid the groundwork for contemporary spallation models and experimental setups. The [[RaLa Experiment\|RaLa (Radioactive Lanthanum) implosion tests]] contributed to an understanding of [[rarefaction]] dynamics and internal fracture in weapon cores.<ref name=":1" /> The development of plate impact methods in the 1960s, including [[light-gas gun]]s and later laser-driven flyers, enabled controlled studies of spall strength across a range of metals and ceramics.<ref name=":0" /> These methodologies have evolved into precise tools used in both defense and scientific applications.		The origins of spall strength studies date back to early [[ballistics\|ballistic]] and explosive experiments in the 20th century. Initial documentation of dynamic fracture can be traced to [[Bertram Hopkinson\|Hopkinson’s]] 1914 experiments.<ref>{{Cite journal \|last=Williams \|first=Cyril Labode \|date=2022-10-05 \|title=Void Mediated Failure at the Extremes: Spallation in Magnesium and Aluminum \|journal=Metals \|language=en \|volume=12 \|issue=10 \|pages=1667 \|doi=10.3390/met12101667 \|doi-access=free \|issn=2075-4701}}</ref> During [[World War II]], extensive research at [[Los Alamos National Laboratory]] under the leadership of [[J. Robert Oppenheimer]] and colleagues investigated shock-induced failure in [[nuclear materials]].<ref>{{Cite journal \|last1=Crockett \|first1=Scott D. \|last2=and Freibert \|first2=Franz J. \|date=2021-12-03 \|title=Equation of State: Manhattan Project Developments and Beyond \|url=https://doi.org/10.1080/00295450.2021.1913036 \|journal=Nuclear Technology \|volume=207 \|issue=sup1 \|pages=S286–S294 \|doi=10.1080/00295450.2021.1913036 \|arxiv=2103.05773 \|bibcode=2021NucTe.207S.286C \|issn=0029-5450}}</ref><ref name=":1">{{Cite journal \|last1=Brown \|first1=Eric N. \|last2=and Borovina \|first2=Dan L. \|date=2021-12-03 \|title=The Trinity High-Explosive Implosion System: The Foundation for Precision Explosive Applications \|url=https://doi.org/10.1080/00295450.2021.1913954 \|journal=Nuclear Technology \|volume=207 \|issue=sup1 \|pages=S204–S221 \|doi=10.1080/00295450.2021.1913954 \|arxiv=2103.05714 \|bibcode=2021NucTe.207S.204B \|issn=0029-5450}}</ref> These efforts laid the groundwork for contemporary spallation models and experimental setups. The [[RaLa Experiment\|RaLa (Radioactive Lanthanum) implosion tests]] contributed to an understanding of [[rarefaction]] dynamics and internal fracture in weapon cores.<ref name=":1" /> The development of plate impact methods in the 1960s, including [[light-gas gun]]s and later laser-driven flyers, enabled controlled studies of spall strength across a range of metals and ceramics.<ref name=":0" /> These methodologies have evolved into precise tools used in both defense and scientific applications.

	==Mechanisms==		==Mechanisms==

wikipedia>Citation bot: Altered bibcode. | Use this bot. Report bugs. | Suggested by Headbomb | Category:CS1 maint: bibcode | #UCB_Category 24/36

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← Older revision		Revision as of 01:52, 11 September 2025
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	==Representative values==		==Representative values==

	Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979}}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|volume=11 \|issue=3 \|pages=398–410 \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM..~~tmp~~...~~13F~~ \|issn=2199-7454\|doi-access=free }}</ref>		Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979}}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|volume=11 \|issue=3 \|pages=398–410 \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM...11..398F \|issn=2199-7454\|doi-access=free }}</ref>

	These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.		These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.

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← Older revision		Revision as of 04:19, 31 August 2025
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	The spall strength of materials is typically measured using high-strain-rate experiments involving impact-induced shock loading. The most prevalent method is the plate impact experiment, where a flyer plate is accelerated—either via gas expansion or [[explosive lens]]—toward a stationary target specimen.<ref name=":0" /> The impact generates a planar shock wave that travels through the material and releases at a free surface to create the tensile pulse necessary for spallation.		The spall strength of materials is typically measured using high-strain-rate experiments involving impact-induced shock loading. The most prevalent method is the plate impact experiment, where a flyer plate is accelerated—either via gas expansion or [[explosive lens]]—toward a stationary target specimen.<ref name=":0" /> The impact generates a planar shock wave that travels through the material and releases at a free surface to create the tensile pulse necessary for spallation.

	In these experiments, the temporal profile of the free-surface velocity is recorded using high-speed diagnostics like [[Velocity interferometer system for any reflector\|Velocity Interferometer System for Any Reflector]] (VISAR)<ref>{{Cite journal \|last1=Tollier \|first1=L. \|last2=Fabbro \|first2=R. \|date=1998-02-01 \|title=Study of the laser-driven spallation process by the VISAR interferometry technique. II. Experiment and simulation of the spallation process \|url=https://doi.org/10.1063/1.366820 \|journal=Journal of Applied Physics \|volume=83 \|issue=3 \|pages=1231–1237 \|doi=10.1063/1.366820 \|bibcode=1998JAP....83.1231T \|issn=0021-8979\|url-access=subscription }}</ref> or [[Photon Doppler Velocimetry]] (PDV).<ref name=":3">{{Cite journal \|last1=Koube \|first1=K. D. \|last2=Kennedy \|first2=G. \|last3=Bertsch \|first3=K. \|last4=Kacher \|first4=J. \|last5=Thoma \|first5=D. J. \|last6=Thadhani \|first6=N. N. \|date=2022-08-23 \|title=Spall damage mechanisms in laser powder bed fabricated stainless steel 316L \|url=https://www.sciencedirect.com/science/article/pii/S0921509322010073 \|journal=Materials Science and Engineering: A \|volume=851 \|article-number=143622 \|doi=10.1016/j.msea.2022.143622 \|issn=0921-5093}}</ref> These laser-based interferometers detect changes in velocity, allowing the identification of the pull-back signal indicative of spall.		In these experiments, the temporal profile of the free-surface velocity is recorded using high-speed diagnostics like [[Velocity interferometer system for any reflector\|Velocity Interferometer System for Any Reflector]] (VISAR)<ref>{{Cite journal \|last1=Tollier \|first1=L. \|last2=Fabbro \|first2=R. \|date=1998-02-01 \|title=Study of the laser-driven spallation process by the VISAR interferometry technique. II. Experiment and simulation of the spallation process \|url=https://doi.org/10.1063/1.366820 \|journal=Journal of Applied Physics \|volume=83 \|issue=3 \|pages=1231–1237 \|doi=10.1063/1.366820 \|bibcode=1998JAP....83.1231T \|issn=0021-8979\|url-access=subscription }}</ref> or [[Photon Doppler Velocimetry]] (PDV).<ref name=":3">{{Cite journal \|last1=Koube \|first1=K. D. \|last2=Kennedy \|first2=G. \|last3=Bertsch \|first3=K. \|last4=Kacher \|first4=J. \|last5=Thoma \|first5=D. J. \|last6=Thadhani \|first6=N. N. \|date=2022-08-23 \|title=Spall damage mechanisms in laser powder bed fabricated stainless steel 316L \|url=https://www.sciencedirect.com/science/article/pii/S0921509322010073 \|journal=Materials Science and Engineering: A \|volume=851 \|article-number=143622 \|doi=10.1016/j.msea.2022.143622 \|osti=1895150 \|issn=0921-5093}}</ref> These laser-based interferometers detect changes in velocity, allowing the identification of the pull-back signal indicative of spall.

	The fundamental equation derived from conservation laws and wave mechanics used in such analyses is:		The fundamental equation derived from conservation laws and wave mechanics used in such analyses is:
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	Advanced plate impact setups include single-stage and two-stage light-gas guns. Two-stage guns can achieve flyer velocities exceeding 7 km/s, generating strain rates beyond <math>10^6\, \text{s}^{-1}</math>.<ref>{{Cite journal \|last1=Suman \|first1=Gaurav \|last2=Bhardwaj \|first2=Vikas \|last3=Dinesh Kumar \|first3=Pal \|date=2025-07-01 \|title=Review of various techniques to achieve velocity unobtainable with two stage light gas gun \|url=https://www.sciencedirect.com/science/article/pii/S0273117725004089 \|journal=Advances in Space Research \|volume=76 \|issue=1 \|pages=469–480 \|doi=10.1016/j.asr.2025.04.054 \|bibcode=2025AdSpR..76..469S \|issn=0273-1177\|url-access=subscription }}</ref> Alternatively, laser-driven flyer plates or direct [[Laser ablation\|ablation]] methods are used to probe ultra-high strain rate regimes (<math>>10^7 \, \text{s}^{-1}</math>). These experiments rely on high-energy pulsed lasers, such as [[Nd:YAG laser\|Nd:YAG]] or [[Titanium-sapphire laser\|Ti:sapphire]] systems, to produce shock pressures in excess of 100 GPa.<ref>{{Cite journal \|last1=Mallick \|first1=D. D. \|last2=Zhao \|first2=M. \|last3=Parker \|first3=J. \|last4=Kannan \|first4=V. \|last5=Bosworth \|first5=B. T. \|last6=Sagapuram \|first6=D. \|last7=Foster \|first7=M. A. \|last8=Ramesh \|first8=K. T. \|date=2019-06-01 \|title=Laser-Driven Flyers and Nanosecond-Resolved Velocimetry for Spall Studies in Thin Metal Foils \|url=https://doi.org/10.1007/s11340-019-00519-x \|journal=Experimental Mechanics \|language=en \|volume=59 \|issue=5 \|pages=611–628 \|doi=10.1007/s11340-019-00519-x \|issn=1741-2765\|url-access=subscription }}</ref><ref>{{Cite journal \|last1=Eliezer \|first1=Shalom \|last2=Gilath \|first2=Irith \|last3=Bar-Noy \|first3=Tuvia \|date=1990-01-15 \|title=Laser-induced spall in metals: Experiment and simulation \|url=https://doi.org/10.1063/1.345777 \|journal=Journal of Applied Physics \|volume=67 \|issue=2 \|pages=715–724 \|doi=10.1063/1.345777 \|bibcode=1990JAP....67..715E \|issn=0021-8979\|url-access=subscription }}</ref>		Advanced plate impact setups include single-stage and two-stage light-gas guns. Two-stage guns can achieve flyer velocities exceeding 7 km/s, generating strain rates beyond <math>10^6\, \text{s}^{-1}</math>.<ref>{{Cite journal \|last1=Suman \|first1=Gaurav \|last2=Bhardwaj \|first2=Vikas \|last3=Dinesh Kumar \|first3=Pal \|date=2025-07-01 \|title=Review of various techniques to achieve velocity unobtainable with two stage light gas gun \|url=https://www.sciencedirect.com/science/article/pii/S0273117725004089 \|journal=Advances in Space Research \|volume=76 \|issue=1 \|pages=469–480 \|doi=10.1016/j.asr.2025.04.054 \|bibcode=2025AdSpR..76..469S \|issn=0273-1177\|url-access=subscription }}</ref> Alternatively, laser-driven flyer plates or direct [[Laser ablation\|ablation]] methods are used to probe ultra-high strain rate regimes (<math>>10^7 \, \text{s}^{-1}</math>). These experiments rely on high-energy pulsed lasers, such as [[Nd:YAG laser\|Nd:YAG]] or [[Titanium-sapphire laser\|Ti:sapphire]] systems, to produce shock pressures in excess of 100 GPa.<ref>{{Cite journal \|last1=Mallick \|first1=D. D. \|last2=Zhao \|first2=M. \|last3=Parker \|first3=J. \|last4=Kannan \|first4=V. \|last5=Bosworth \|first5=B. T. \|last6=Sagapuram \|first6=D. \|last7=Foster \|first7=M. A. \|last8=Ramesh \|first8=K. T. \|date=2019-06-01 \|title=Laser-Driven Flyers and Nanosecond-Resolved Velocimetry for Spall Studies in Thin Metal Foils \|url=https://doi.org/10.1007/s11340-019-00519-x \|journal=Experimental Mechanics \|language=en \|volume=59 \|issue=5 \|pages=611–628 \|doi=10.1007/s11340-019-00519-x \|issn=1741-2765\|url-access=subscription }}</ref><ref>{{Cite journal \|last1=Eliezer \|first1=Shalom \|last2=Gilath \|first2=Irith \|last3=Bar-Noy \|first3=Tuvia \|date=1990-01-15 \|title=Laser-induced spall in metals: Experiment and simulation \|url=https://doi.org/10.1063/1.345777 \|journal=Journal of Applied Physics \|volume=67 \|issue=2 \|pages=715–724 \|doi=10.1063/1.345777 \|bibcode=1990JAP....67..715E \|issn=0021-8979\|url-access=subscription }}</ref>

	Post-shock characterization plays a crucial role in verifying spall damage. [[Scanning electron microscopy]] (SEM), [[transmission electron microscopy]] (TEM), and [[X-ray microtomography]] are employed to visualize voids, microcracks, and plastic deformation patterns. Cross-sectional analysis of recovered samples reveals the location of spall planes and allows correlation of microstructural features with dynamic fracture behavior.<ref name=":0" /><ref name=":5">{{Cite journal \|last1=Lamb \|first1=K. \|last2=Koube \|first2=K. \|last3=Kacher \|first3=J. \|last4=Sloop \|first4=T. \|last5=Thadhani \|first5=N. \|last6=Babu \|first6=S. S. \|date=2023-03-25 \|title=Anisotropic spall failure of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S2214860423000775 \|journal=Additive Manufacturing \|volume=66 \|article-number=103464 \|doi=10.1016/j.addma.2023.103464 \|issn=2214-8604}}</ref><ref name=":4">{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Ndefru \|first3=B. G. \|last4=Martinez \|first4=D. T. \|last5=Trujillo \|first5=C. P. \|last6=Gray \|first6=G. T., III \|date=2018-12-10 \|title=Spall fracture in additive manufactured tantalum \|url=https://doi.org/10.1063/1.5063930 \|journal=Journal of Applied Physics \|volume=124 \|issue=22 \|pages=225902 \|doi=10.1063/1.5063930 \|bibcode=2018JAP...124v5902J \|osti=1489965 \|issn=0021-8979}}</ref><ref>{{Cite book \|last1=Bingert \|first1=John F. \|last2=Suter \|first2=Robert M. \|last3=Lind \|first3=Jonathan \|last4=Li \|first4=Shiu Fai \|last5=Pokharel \|first5=Reeju \|last6=Trujillo \|first6=Carl P. \|chapter=High-Energy Diffraction Microscopy Characterization of Spall Damage \|series=Conference Proceedings of the Society for Experimental Mechanics Series \|date=2014 \|editor-last=Song \|editor-first=Bo \|editor2-last=Casem \|editor2-first=Dan \|editor3-last=Kimberley \|editor3-first=Jamie \|title=Dynamic Behavior of Materials, Volume 1 \|chapter-url=https://link.springer.com/chapter/10.1007/978-3-319-00771-7_48 \|language=en \|location=Cham \|publisher=Springer International Publishing \|pages=397–403 \|doi=10.1007/978-3-319-00771-7_48 \|isbn=978-3-319-00771-7}}</ref>		Post-shock characterization plays a crucial role in verifying spall damage. [[Scanning electron microscopy]] (SEM), [[transmission electron microscopy]] (TEM), and [[X-ray microtomography]] are employed to visualize voids, microcracks, and plastic deformation patterns. Cross-sectional analysis of recovered samples reveals the location of spall planes and allows correlation of microstructural features with dynamic fracture behavior.<ref name=":0" /><ref name=":5">{{Cite journal \|last1=Lamb \|first1=K. \|last2=Koube \|first2=K. \|last3=Kacher \|first3=J. \|last4=Sloop \|first4=T. \|last5=Thadhani \|first5=N. \|last6=Babu \|first6=S. S. \|date=2023-03-25 \|title=Anisotropic spall failure of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S2214860423000775 \|journal=Additive Manufacturing \|volume=66 \|article-number=103464 \|doi=10.1016/j.addma.2023.103464 \|osti=1984432 \|issn=2214-8604}}</ref><ref name=":4">{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Ndefru \|first3=B. G. \|last4=Martinez \|first4=D. T. \|last5=Trujillo \|first5=C. P. \|last6=Gray \|first6=G. T., III \|date=2018-12-10 \|title=Spall fracture in additive manufactured tantalum \|url=https://doi.org/10.1063/1.5063930 \|journal=Journal of Applied Physics \|volume=124 \|issue=22 \|pages=225902 \|doi=10.1063/1.5063930 \|bibcode=2018JAP...124v5902J \|osti=1489965 \|issn=0021-8979}}</ref><ref>{{Cite book \|last1=Bingert \|first1=John F. \|last2=Suter \|first2=Robert M. \|last3=Lind \|first3=Jonathan \|last4=Li \|first4=Shiu Fai \|last5=Pokharel \|first5=Reeju \|last6=Trujillo \|first6=Carl P. \|chapter=High-Energy Diffraction Microscopy Characterization of Spall Damage \|series=Conference Proceedings of the Society for Experimental Mechanics Series \|date=2014 \|editor-last=Song \|editor-first=Bo \|editor2-last=Casem \|editor2-first=Dan \|editor3-last=Kimberley \|editor3-first=Jamie \|title=Dynamic Behavior of Materials, Volume 1 \|chapter-url=https://link.springer.com/chapter/10.1007/978-3-319-00771-7_48 \|language=en \|location=Cham \|publisher=Springer International Publishing \|pages=397–403 \|doi=10.1007/978-3-319-00771-7_48 \|isbn=978-3-319-00771-7}}</ref>

	==Influencing factors==		==Influencing factors==
Line 73:		Line 73:
	where <math>Q</math> is the activation energy for diffusion, <math>R</math> is the [[gas constant]], and <math>T</math> is the absolute temperature.<ref name=":0" />		where <math>Q</math> is the activation energy for diffusion, <math>R</math> is the [[gas constant]], and <math>T</math> is the absolute temperature.<ref name=":0" />

	Material anisotropy and heterogeneity can significantly influence spall behavior. For example, additively manufactured metals often contain porosity, [[residual stress]]es, and texture that reduce spall strength.<ref>{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Dippo \|first3=O. \|last4=Beal \|first4=R. A. \|last5=Livescu \|first5=V. \|last6=Martinez \|first6=D. T. \|last7=Trujillo \|first7=C. P. \|last8=Florando \|first8=J. N. \|last9=Kumar \|first9=M. \|last10=Gray \|first10=G. T., III \|date=2016-10-04 \|title=Spall fracture in additive manufactured Ti-6Al-4V \|url=https://doi.org/10.1063/1.4963279 \|journal=Journal of Applied Physics \|volume=120 \|issue=13 \|pages=135902 \|doi=10.1063/1.4963279 \|bibcode=2016JAP...120m5902J \|osti=1328489 \|issn=0021-8979}}</ref><ref name=":3" /> [[High-entropy alloys]] and [[amorphous metals]], with their complex microstructures and high defect tolerance, show promise for improved performance under extreme loading.<ref name=":6">{{Cite journal \|last1=Thürmer \|first1=Daniel \|last2=Zhao \|first2=Shiteng \|last3=Deluigi \|first3=Orlando R. \|last4=Stan \|first4=Camelia \|last5=Alhafez \|first5=Iyad Alabd \|last6=Urbassek \|first6=Herbert M. \|last7=Meyers \|first7=Marc A. \|last8=Bringa \|first8=Eduardo M. \|last9=Gunkelmann \|first9=Nina \|date=2022-02-25 \|title=Exceptionally high spallation strength for a high-entropy alloy demonstrated by experiments and simulations \|url=https://www.sciencedirect.com/science/article/pii/S0925838821039773 \|journal=Journal of Alloys and Compounds \|volume=895 \|article-number=162567 \|doi=10.1016/j.jallcom.2021.162567 \|issn=0925-8388}}</ref><ref name=":7">{{Cite journal \|last1=Yuan \|first1=Fuping \|last2=Prakash \|first2=Vikas \|last3=Lewandowski \|first3=John J. \|date=2007-02-01 \|title=Spall strength and Hugoniot elastic limit of a zirconium-based bulk metallic glass under planar shock compression \|url=https://doi.org/10.1557/jmr.2007.0053 \|journal=Journal of Materials Research \|language=en \|volume=22 \|issue=2 \|pages=402–411 \|doi=10.1557/jmr.2007.0053 \|bibcode=2007JMatR..22..402Y \|issn=2044-5326\|url-access=subscription }}</ref> Accurate prediction of spall strength thus requires detailed understanding of both the material’s intrinsic properties and the external loading conditions.		Material anisotropy and heterogeneity can significantly influence spall behavior. For example, additively manufactured metals often contain porosity, [[residual stress]]es, and texture that reduce spall strength.<ref>{{Cite journal \|last1=Jones \|first1=D. R. \|last2=Fensin \|first2=S. J. \|last3=Dippo \|first3=O. \|last4=Beal \|first4=R. A. \|last5=Livescu \|first5=V. \|last6=Martinez \|first6=D. T. \|last7=Trujillo \|first7=C. P. \|last8=Florando \|first8=J. N. \|last9=Kumar \|first9=M. \|last10=Gray \|first10=G. T., III \|date=2016-10-04 \|title=Spall fracture in additive manufactured Ti-6Al-4V \|url=https://doi.org/10.1063/1.4963279 \|journal=Journal of Applied Physics \|volume=120 \|issue=13 \|pages=135902 \|doi=10.1063/1.4963279 \|bibcode=2016JAP...120m5902J \|osti=1328489 \|issn=0021-8979}}</ref><ref name=":3" /> [[High-entropy alloys]] and [[amorphous metals]], with their complex microstructures and high defect tolerance, show promise for improved performance under extreme loading.<ref name=":6">{{Cite journal \|last1=Thürmer \|first1=Daniel \|last2=Zhao \|first2=Shiteng \|last3=Deluigi \|first3=Orlando R. \|last4=Stan \|first4=Camelia \|last5=Alhafez \|first5=Iyad Alabd \|last6=Urbassek \|first6=Herbert M. \|last7=Meyers \|first7=Marc A. \|last8=Bringa \|first8=Eduardo M. \|last9=Gunkelmann \|first9=Nina \|date=2022-02-25 \|title=Exceptionally high spallation strength for a high-entropy alloy demonstrated by experiments and simulations \|url=https://www.sciencedirect.com/science/article/pii/S0925838821039773 \|journal=Journal of Alloys and Compounds \|volume=895 \|article-number=162567 \|doi=10.1016/j.jallcom.2021.162567 \|osti=1843121 \|issn=0925-8388}}</ref><ref name=":7">{{Cite journal \|last1=Yuan \|first1=Fuping \|last2=Prakash \|first2=Vikas \|last3=Lewandowski \|first3=John J. \|date=2007-02-01 \|title=Spall strength and Hugoniot elastic limit of a zirconium-based bulk metallic glass under planar shock compression \|url=https://doi.org/10.1557/jmr.2007.0053 \|journal=Journal of Materials Research \|language=en \|volume=22 \|issue=2 \|pages=402–411 \|doi=10.1557/jmr.2007.0053 \|bibcode=2007JMatR..22..402Y \|issn=2044-5326\|url-access=subscription }}</ref> Accurate prediction of spall strength thus requires detailed understanding of both the material’s intrinsic properties and the external loading conditions.

	==Representative values==		==Representative values==
Line 86:		Line 86:
	==Current research thrusts==		==Current research thrusts==

	Ongoing research in spall strength is focused on advanced materials and improved characterization techniques. [[Additive manufacturing]] has introduced new challenges and opportunities; researchers aim to understand how layer-wise construction, residual stresses, and porosity influence spall behavior.<ref name=":5" /><ref>{{Cite journal \|last1=Gray \|first1=G. T. \|last2=Livescu \|first2=V. \|last3=Rigg \|first3=P. A. \|last4=Trujillo \|first4=C. P. \|last5=Cady \|first5=C. M. \|last6=Chen \|first6=S. R. \|last7=Carpenter \|first7=J. S. \|last8=Lienert \|first8=T. J. \|last9=Fensin \|first9=S. J. \|date=2017-10-01 \|title=Structure/property (constitutive and spallation response) of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S1359645417306158 \|journal=Acta Materialia \|volume=138 \|pages=140–149 \|doi=10.1016/j.actamat.2017.07.045 \|bibcode=2017AcMat.138..140G \|issn=1359-6454}}</ref> Computational modeling is becoming increasingly multiscale, coupling [[molecular dynamics\|atomistic simulations]] with [[continuum mechanics]] to predict spall initiation and evolution.<ref>{{Cite journal \|last1=Wang \|first1=Xin-Xin \|last2=He \|first2=An-Min \|last3=Zhou \|first3=Ting-Ting \|last4=Wang \|first4=Pei \|date=2021-09-01 \|title=Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation \|url=https://www.sciencedirect.com/science/article/pii/S0167663621002246 \|journal=Mechanics of Materials \|volume=160 \|article-number=103991 \|doi=10.1016/j.mechmat.2021.103991 \|bibcode=2021MechM.16003991W \|issn=0167-6636\|url-access=subscription }}</ref> In-situ diagnostics, such as ultrafast X-ray imaging at [[synchrotrons]] or [[Free-electron laser\|XFELs]], provide real-time observations of void dynamics during spall events.<ref>{{Cite journal \|last1=Wang \|first1=Xiaoming \|last2=Rigg \|first2=Paulo \|last3=Sethian \|first3=John \|last4=Sinclair \|first4=Nicholas \|last5=Weir \|first5=Nicholas \|last6=Williams \|first6=Brendan \|last7=Zhang \|first7=Jun \|last8=Hawreliak \|first8=James \|last9=Toyoda \|first9=Yoshimasa \|last10=Gupta \|first10=Yogendra \|last11=Li \|first11=Yuelin \|last12=Broege \|first12=Douglas \|last13=Bromage \|first13=Jake \|last14=Earley \|first14=Robert \|last15=Guy \|first15=Dale \|date=2019-05-10 \|title=The laser shock station in the dynamic compression sector. I \|url=https://doi.org/10.1063/1.5088367 \|journal=Review of Scientific Instruments \|volume=90 \|issue=5 \|pages=053901 \|doi=10.1063/1.5088367 \|pmid=31153279 \|bibcode=2019RScI...90e3901W \|osti=1542978 \|issn=0034-6748}}</ref><ref>{{Cite journal \|last1=Flanagan \|first1=R. M. \|last2=Fensin \|first2=S. J. \|last3=Meyers \|first3=M. A. \|date=2022-01-19 \|title=The role of pre-existing heterogeneities in materials under shock and spall \|url=https://doi.org/10.1063/5.0053693 \|journal=Applied Physics Reviews \|volume=9 \|issue=1 \|pages=011305 \|doi=10.1063/5.0053693 \|bibcode=2022ApPRv...9a1305F \|osti=1841029 \|issn=1931-9401}}</ref> These experiments are helping to refine constitutive models and damage criteria.		Ongoing research in spall strength is focused on advanced materials and improved characterization techniques. [[Additive manufacturing]] has introduced new challenges and opportunities; researchers aim to understand how layer-wise construction, residual stresses, and porosity influence spall behavior.<ref name=":5" /><ref>{{Cite journal \|last1=Gray \|first1=G. T. \|last2=Livescu \|first2=V. \|last3=Rigg \|first3=P. A. \|last4=Trujillo \|first4=C. P. \|last5=Cady \|first5=C. M. \|last6=Chen \|first6=S. R. \|last7=Carpenter \|first7=J. S. \|last8=Lienert \|first8=T. J. \|last9=Fensin \|first9=S. J. \|date=2017-10-01 \|title=Structure/property (constitutive and spallation response) of additively manufactured 316L stainless steel \|url=https://www.sciencedirect.com/science/article/pii/S1359645417306158 \|journal=Acta Materialia \|volume=138 \|pages=140–149 \|doi=10.1016/j.actamat.2017.07.045 \|bibcode=2017AcMat.138..140G \|osti=1463491 \|issn=1359-6454}}</ref> Computational modeling is becoming increasingly multiscale, coupling [[molecular dynamics\|atomistic simulations]] with [[continuum mechanics]] to predict spall initiation and evolution.<ref>{{Cite journal \|last1=Wang \|first1=Xin-Xin \|last2=He \|first2=An-Min \|last3=Zhou \|first3=Ting-Ting \|last4=Wang \|first4=Pei \|date=2021-09-01 \|title=Spall damage in single crystal tin under shock wave loading: A molecular dynamics simulation \|url=https://www.sciencedirect.com/science/article/pii/S0167663621002246 \|journal=Mechanics of Materials \|volume=160 \|article-number=103991 \|doi=10.1016/j.mechmat.2021.103991 \|bibcode=2021MechM.16003991W \|issn=0167-6636\|url-access=subscription }}</ref> In-situ diagnostics, such as ultrafast X-ray imaging at [[synchrotrons]] or [[Free-electron laser\|XFELs]], provide real-time observations of void dynamics during spall events.<ref>{{Cite journal \|last1=Wang \|first1=Xiaoming \|last2=Rigg \|first2=Paulo \|last3=Sethian \|first3=John \|last4=Sinclair \|first4=Nicholas \|last5=Weir \|first5=Nicholas \|last6=Williams \|first6=Brendan \|last7=Zhang \|first7=Jun \|last8=Hawreliak \|first8=James \|last9=Toyoda \|first9=Yoshimasa \|last10=Gupta \|first10=Yogendra \|last11=Li \|first11=Yuelin \|last12=Broege \|first12=Douglas \|last13=Bromage \|first13=Jake \|last14=Earley \|first14=Robert \|last15=Guy \|first15=Dale \|date=2019-05-10 \|title=The laser shock station in the dynamic compression sector. I \|url=https://doi.org/10.1063/1.5088367 \|journal=Review of Scientific Instruments \|volume=90 \|issue=5 \|pages=053901 \|doi=10.1063/1.5088367 \|pmid=31153279 \|bibcode=2019RScI...90e3901W \|osti=1542978 \|issn=0034-6748}}</ref><ref>{{Cite journal \|last1=Flanagan \|first1=R. M. \|last2=Fensin \|first2=S. J. \|last3=Meyers \|first3=M. A. \|date=2022-01-19 \|title=The role of pre-existing heterogeneities in materials under shock and spall \|url=https://doi.org/10.1063/5.0053693 \|journal=Applied Physics Reviews \|volume=9 \|issue=1 \|pages=011305 \|doi=10.1063/5.0053693 \|bibcode=2022ApPRv...9a1305F \|osti=1841029 \|issn=1931-9401}}</ref> These experiments are helping to refine constitutive models and damage criteria.

	Researchers are also exploring novel material systems, including high-entropy alloys, [[metallic glasses]], and [[bioinspired composites]], for enhanced dynamic strength.<ref name=":6" /><ref name=":7" /><ref>{{Cite journal \|last1=Wu \|first1=Gang \|last2=Wang \|first2=Xin \|last3=Wang \|first3=Yuting \|last4=Ji \|first4=Chong \|last5=Zhao \|first5=Changxiao \|last6=Gao \|first6=Yuxuan \|date=2023-10-01 \|title=Blast response of bioinspired nacre-like staggered composite plates combined with steel and polyurea \|url=https://www.sciencedirect.com/science/article/pii/S0734743X23002294 \|journal=International Journal of Impact Engineering \|volume=180 \|article-number=104719 \|doi=10.1016/j.ijimpeng.2023.104719 \|bibcode=2023IJIE..18004719W \|issn=0734-743X\|url-access=subscription }}</ref> The integration of [[machine learning]] into material design workflows is being used to predict spall performance across compositional and processing spaces.<ref>{{Cite journal \|last1=Frawley \|first1=Keara G. \|last2=Thadhani \|first2=Naresh N. \|last3=Ramprasad \|first3=Rampi \|last4=Sahu \|first4=Harikrishna \|date=2025-03-12 \|title=A machine learning approach to predicting the spall strength of metals and alloys \|journal=Journal of Applied Physics \|volume=137 \|issue=10 \|pages=104905 \|doi=10.1063/5.0248560 \|bibcode=2025JAP...137j4905F \|issn=0021-8979\|doi-access=free }}</ref> As a result, spall strength research continues to evolve at the intersection of materials science, mechanics, and data-driven engineering.		Researchers are also exploring novel material systems, including high-entropy alloys, [[metallic glasses]], and [[bioinspired composites]], for enhanced dynamic strength.<ref name=":6" /><ref name=":7" /><ref>{{Cite journal \|last1=Wu \|first1=Gang \|last2=Wang \|first2=Xin \|last3=Wang \|first3=Yuting \|last4=Ji \|first4=Chong \|last5=Zhao \|first5=Changxiao \|last6=Gao \|first6=Yuxuan \|date=2023-10-01 \|title=Blast response of bioinspired nacre-like staggered composite plates combined with steel and polyurea \|url=https://www.sciencedirect.com/science/article/pii/S0734743X23002294 \|journal=International Journal of Impact Engineering \|volume=180 \|article-number=104719 \|doi=10.1016/j.ijimpeng.2023.104719 \|bibcode=2023IJIE..18004719W \|issn=0734-743X\|url-access=subscription }}</ref> The integration of [[machine learning]] into material design workflows is being used to predict spall performance across compositional and processing spaces.<ref>{{Cite journal \|last1=Frawley \|first1=Keara G. \|last2=Thadhani \|first2=Naresh N. \|last3=Ramprasad \|first3=Rampi \|last4=Sahu \|first4=Harikrishna \|date=2025-03-12 \|title=A machine learning approach to predicting the spall strength of metals and alloys \|journal=Journal of Applied Physics \|volume=137 \|issue=10 \|pages=104905 \|doi=10.1063/5.0248560 \|bibcode=2025JAP...137j4905F \|issn=0021-8979\|doi-access=free }}</ref> As a result, spall strength research continues to evolve at the intersection of materials science, mechanics, and data-driven engineering.

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← Older revision		Revision as of 04:28, 20 August 2025
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	==Representative values==		==Representative values==

	Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979}}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM..tmp...13F \|issn=2199-7454\|doi-access=free }}</ref>		Spall strength varies significantly between material classes due to differences in bonding, microstructure, and deformation mechanisms. Representative values are typically reported in gigapascals (GPa) for [[metals]] and [[ceramics]], and megapascals (MPa) for [[polymers]]. For example, high-purity [[copper]] exhibits spall strengths around 1.2–1.6 GPa at moderate strain rates,<ref>{{Cite journal \|last1=Minich \|first1=Roger W. \|last2=Cazamias \|first2=James U. \|last3=Kumar \|first3=Mukui \|last4=Schwartz \|first4=Adam J. \|date=2004-09-01 \|title=Effect of microstructural length scales on spall behavior of copper \|url=https://doi.org/10.1007/s11661-004-0212-7 \|journal=Metallurgical and Materials Transactions A \|language=en \|volume=35 \|issue=9 \|pages=2663–2673 \|doi=10.1007/s11661-004-0212-7 \|bibcode=2004MMTA...35.2663M \|issn=1543-1940\|url-access=subscription }}</ref> while [[tantalum]] and [[tungsten]] can reach 3–5 GPa under similar conditions.<ref name=":4" /><ref>{{Cite journal \|last1=Zurek \|first1=A. K. \|last2=Iii \|first2=G. T. Gray \|date=1991-10-01 \|title=Dynamic Strength and Strain Rate Effects on Fracture Behavior of Tungsten and Tungsten Alloys \|url=http://dx.doi.org/10.1051/jp4:1991388 \|journal=Le Journal de Physique IV \|language=en \|volume=01 \|issue=C3 \|pages=C3–637 \|doi=10.1051/jp4:1991388 \|issn=1155-4339}}</ref> Ceramics such as [[alumina]] and [[silicon carbide]] often exhibit brittle spall behavior with values ranging from 0.5–2.0 GPa.<ref>{{Cite journal \|last1=Murray \|first1=N. H. \|last2=Bourne \|first2=N. K. \|last3=Rosenberg \|first3=Z. \|last4=Field \|first4=J. E. \|date=1998-07-15 \|title=The spall strength of alumina ceramics \|url=https://doi.org/10.1063/1.368130 \|journal=Journal of Applied Physics \|volume=84 \|issue=2 \|pages=734–738 \|doi=10.1063/1.368130 \|bibcode=1998JAP....84..734M \|issn=0021-8979}}</ref><ref>{{Cite journal \|last=Dandekar \|first=Dattatraya P. \|date=2004 \|title=Spall Strength of Silicon Carbide Under Normal and Simultaneous Compression-Shear Shock Wave Loading \|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7402.2004.tb00178.x \|journal=International Journal of Applied Ceramic Technology \|language=en \|volume=1 \|issue=3 \|pages=261–268 \|doi=10.1111/j.1744-7402.2004.tb00178.x \|issn=1744-7402\|url-access=subscription }}</ref> Polymers like [[Poly(methyl methacrylate)\|PMMA]] and [[polycarbonate]] have much lower spall strengths, typically in the range of 20–100 MPa.<ref>{{Cite journal \|last1=Frawley \|first1=K. G. \|last2=Kennedy \|first2=G. \|last3=Jordan \|first3=J. L. \|last4=Ramprasad \|first4=R. \|last5=Thadhani \|first5=N. N. \|date=2025-03-12 \|title=Dynamic Spall Failure of Polymers \|journal=Journal of Dynamic Behavior of Materials \|volume=11 \|issue=3 \|pages=398–410 \|language=en \|doi=10.1007/s40870-025-00468-8 \|bibcode=2025JDBM..tmp...13F \|issn=2199-7454\|doi-access=free }}</ref>

	These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.		These values are sensitive to strain rate, specimen purity, and experimental configuration. In practice, tabulated datasets compiled from controlled experiments or simulations are used to benchmark and calibrate spall models.