A crack tip driving force model for mode I crack propagation along linear strength gradient: comparison with the sharp strength gradient case

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• 作者：Yi-Bo Shang ; Hui-Ji Shi ; Zhao-Xi Wang ; Guo-Dong Zhang
• 刊名：Acta Mechanica
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：227
• 期：9
• 页码：2683-2702
• 全文大小：4,619 KB
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics, Fluids and Thermodynamics
  Continuum Mechanics and Mechanics of Materials
  Structural Mechanics
  Vibration, Dynamical Systems and Control
  Engineering Thermodynamics and Transport Phenomena
  
• 出版者：Springer Wien
• ISSN：1619-6937
• 卷排序：227

文摘

In the present work, based on the Dugdale criterion, a closed-form theoretical crack tip driving force model of simple expressions was proposed for static and fatigue crack propagation along a linear yield strength gradient (YSG). Qualitative and quantitative analyses of the YSG effect on the crack tip driving force are given. The crack tip driving force depends on the yield strength at the crack tip, the YSG within the plastic zone and the applied load. A positive (or negative) YSG has a shielding (or amplifying) effect on the crack tip driving force. A difference of material-toughening mechanisms between smooth and sharp strength gradient was revealed both theoretically and numerically. In the linear YSG case, when a fatigue crack propagates along the YSG at a constant applied cyclic crack tip stress intensity factor, the cyclic crack tip opening displacement decreases (or increases) when the crack propagates towards a higher (or lower)-strength region; however, the cyclic crack tip stress intensity factor increases, no matter when the crack propagates towards a higher- or lower-strength region. This abnormal phenomenon causes theoretical and experimental challenges for characterizing the smooth strength gradient effect on the crack tip driving force.AbbreviationsaDistance between crack tip and interface\(C_{\mathrm{inh}}\)Additional material inhomogeneity termCPS88-Node biquadratic plane stress quadrilateral elementCTCompact tensionCTODCrack tip opening displacementDCBDouble cantilever beamEYoung’s modulusFCPFatigue crack propagationFEMFinite element method\(G_{\mathrm{applied}}\)Applied energy release rateJJ-integral\(J_{\mathrm{applied}}\)Applied J-integral\(J_{\mathrm{tip}}\)Crack tip J-integralkYield strength gradientKStress intensity factor\(K_{\mathrm{applied}}\)Applied stress intensity factor\(K_{\mathrm{cohesive}}\)Cohesive stress intensity factor\(K_{\mathrm{tip}}\)Crack tip stress intensity factorlDistance between interface and mathematical crack tip\(p_{\infty }\)Monotonic far field load\(P_{\mathrm{applied}}\)Applied load per thickness\(r_{\mathrm{hom}}\)Crack tip plastic zone size (or Dugdale cohesive zone size) in homogeneous materialrCrack tip plastic zone size (or Dugdale cohesive zone size) in YSG case\(r^{\prime }\)Radius of crack tip circular plastic zonevPoisson’s ratioWSpecimen widthYSGYield strength gradient\(\alpha \)Ratio of crack length to specimen width\(\varGamma _{\mathrm{cz}}\)Integration contour for J-integral\(\delta \)Crack opening displacement\(\Delta \)Parameter under cyclic or fatigue load\(\varphi (z)\)Complex potential\({\sigma }^{\mathrm{A}}\)Yield stress of material A in plane stress condition\(\sigma ^{\mathrm{B}}\)Yield stress of material B in plane stress condition\(\sigma _{\mathrm{s}}\)Yield stress\(\sigma _{0}\)Cohesive stress at crack tip\(\upsilon \)Crack opening displacement in the y direction from the crack axis in the cohesive zone