This article presents development of a damage-coupled viscoplastic constitutive model with temperature consideration. The model is subjected to an explicit nonlocal treatment within the characteristic length that is not limited to one local element as conventional ones. Temperature dependence of material behavior is incorporated into the model to account for the material property degradation at elevated temperature. A test program to determine the correlation between material parameters and temperature is also presented. The nonlocal damage-coupled viscoplastic material model is implemented in a commercial finite element program ABAQUS through its user-defined material subroutine UMAT using a semi-implicit time integration scheme. The model is applied to predict the behavior of 63Sn37Pb soldered structure. The mesh sensitivity of the model is discussed, as well as the efficiency of deduced consistent tangent modulus.
LoweTMillerA. Improved constitutive equations for modeling strain softening, parts I and II. J Eng Mater: T ASME1984; 106(4): 337–348.
2.
WeiYChowCFangH. Characteristics of creep damage for 60 Sn–40 Pb solder material. J Electron Packaging2001; 123: 278–283.
3.
WeiYChowCNeilsenM. Failure analysis of solder joints with a damage-coupled viscoplastic model. Int J Numer Meth Eng2003; 56: 2199–2211.
4.
YangXNassarS. Constitutive modeling of time-dependent cyclic straining for solder alloy 63Sn–37Pb. Mech Mater2005; 37: 801–814.
5.
MaoJ. Nonlocal damage gradient model for structural analysis. Master’s Thesis, University of Michigan-Dearborn, Dearborn, MI, 2010.
6.
BasaranCZhaoYTangH. A damage-mechanics-based constitutive model for solder joints. J Electron Packaging2005; 127: 208–214.
7.
JieMChengCChowC. Forming limit diagrams of strain-rate-dependent sheet metals. Int J Mech Sci2009; 51(4): 269–275.
8.
ChabocheJ. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plasticity1989; 5: 247–302.
9.
KobayashiMMukaiMTakahashiH. Implicit integration and consistent tangent modulus of a time-dependent non-unified constitutive model. Int J Numer Meth Eng2003; 58: 1523–1543.
10.
KulligEWipplerS. Numerical integration and FEM-implementation of a viscoplastic Chaboche-model with static recovery. Comput Mech2006; 38(6): 1–13.
11.
KangG. Finite element implementation of a visco-plastic constitutive model with strain-range-dependent cyclic hardening. Commun Numer Meth En2006; 22(2): 137–153.
12.
DmitriKBinningPSloanSW. Truncation error and stability analysis of iterative and non-iterative Thomas-Gladwell methods for first-order non-linear differential equations. Int J Numer Meth Eng2004; 60(12): 2031–2043.
13.
CaoJLinJDeanTA. An implicit unitless error and step-size control method in integrating unified viscoplastic/creep ODE-type constitutive equations. Int J Numer Meth Eng2008; 73: 1094–1112.
14.
LinJDunneFPEHayhurstDR. Approximate method for the analysis of components undergoing ratchetting and failure. J Strain Anal Eng1988; 33: 55–65.
15.
ShenJMaoJBoileauJ. Material damage evaluation with measured microdefects and multiresolution numerical analysis. Int J Damage Mech. Epub ahead of print 28August2013. DOI: 1056789513501913.
ChowCMaoJShenJ. Nonlocal damage gradient model for fracture characterization of aluminum alloy. Int J Damage Mech2011; 20: 1073–1093.
22.
KowalskyUMeyerJHeinrichS. A nonlocal damage model for mild steel under inelastic cyclic straining. Comp Mater Sci2012; 63: 28–34.
23.
YangXChowCLauK. Time-dependent cyclic deformation and failure of 63Sn/37Pb solder alloy. Int J Fatigue2003; 25: 533–546.
24.
MurakamiS. Notion of continuum damage mechanics and its application to anisotropic creep damage theory. J Eng Mater: T ASME1983; 105: 99–105.
25.
ShenJMaoJReyesG. A multiresolution transformation rule of material defects. Int J Damage Mech2009; 18: 739–758.
26.
ChowCLWeiY. Constitutive modeling of material damage for fatigue failure prediction. Int J Damage Mech1999; 8: 355–375.
27.
YangXChowCLauK. A unified viscoplastic fatigue damage model for 63Sn-37Pb solder alloy under cyclic stress control. Int J Damage Mech2003; 12: 225–243.
28.
NassarSMaoJYangX. Effect of adhesives on the mechanical behavior of thick composite joints. In: ASME pressure vessels and piping conference (PVP2011), Baltimore, MD, 17–21 July 2011, pp.3–11. New York: ASME.
29.
NassarSMaoJYangX. A damage model for adhesively bonded single-lap thick composite joints. J Eng Mater: T ASME2012; 134: 041004.1–041004.7.
30.
MaoJYangXGaoQ. Finite element implementation of time-dependent constitutive model of solder in micro-electronic packaging. J Eng Mech: ASCE2009; 26(7): 216–221.
31.
MaoJNassarSYangX. An improved model for adhesively bonded DCB joints. J Adhes Sci Technol2014; 28(6): 613–629.
32.
MaoJNassarS. Assessment of different joining techniques for dissimilar materials. SAE technical paper 2014-01-0790, 2014.
33.
ChowCLLuTL. On evolution laws of anisotropic damage. Eng Fract Mech1989; 34: 679–701.
34.
FrederickCOArmstrongPJ. A mathematical representation of the multiaxial Bauschinger effect. Mater High Temp2007; 24(1): 1–26.
35.
ShaoEYangXMaoJ. Experimental study on kinematic hardening of 1Cr18Ni9Ti stainless steel under low cyclic fatigue. Nucl Power En2006; 27(3): 32–36.
36.
ABAQUS. User subroutines reference manual (Version 6.11). Providence, RI, USA: Hibbitt Karlsson and Sorensen Inc., 2012.
37.
MaoJYangXGaoQ. Experimental study of 63Sn-37Pb solder alloy under uniaxial loading at high temperature. Nonferrous Met2008; 60(3): 5–9.
38.
MaoJEngler-PintoCSuX. Cyclic behavior of an Al-Si-Cu alloy under thermo-mechanical loading. Int J Mater Manf2014; 7(3). DOI: 10.4271/2014-01-1012.
39.
MaoJ. Time-dependent damage coupled constitutive model of solder alloy in microelectronic packing at high temperature and its application. Master’s Thesis, Southwest Jiaotong University, Chengdu, China, 2007.
