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Peter I. Kattan - One of the best experts on this subject based on the ideXlab platform.
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Some Basic Issues of Isotropic and Anisotropic Continuum Damage Mechanics
Handbook of Damage Mechanics, 2021Co-Authors: George Z. Voyiadjis, Peter I. Kattan, Mohammed A. YousefAbstract:This chapter includes two main topics in isotropic and anisotropic Damage mechanics. In the first topic, various new proposed Damage variables are introduced, examined, and compared. The scalar case pertaining to isotropic Damage is investigated, and several types of new Damage variables are proposed. The Damage variables introduced in this part can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. Moreover, higher-order strain energy forms are proposed. These higher-order strain energy forms along with some of the proposed Damage variables are used in trying to lay the theoretical groundwork for the design of unDamageable materials, i.e., materials that cannot be Damaged where the value of the Damage variable remains zero throughout the deformation process.The second topic presents a new concept of anisotropic Damage that is examined within the framework of continuum Damage mechanics. New proposed Damage Tensors are studied in order to investigate the Damage Effect variables in the mechanical behavior of materials. In addition, new hybrid Damage Tensors are proposed and defined in terms of the Damage Effect Tensor and the new proposed Damage Tensors. Accordingly, this study demonstrates that most of the new proposed Damage Tensors are verified within the framework of continuum Damage mechanics.
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new Tensors for anisotropic Damage in continuum Damage mechanics
Journal of Engineering Materials and Technology-transactions of The Asme, 2012Co-Authors: George Z. Voyiadjis, Mohammed A. Yousef, Peter I. KattanAbstract:In this work, new proposed Damage Tensors are studied in order to investigate the Damage Effect variables in the mechanical behavior of materials. All cases studied in this work are defined in terms of the elasticity of the material and based on the hypotheses of both elastic strain equivalence and elastic energy equivalence. Moreover, the new proposed Damage Tensors are anisotropically expressed in terms of the well-known Damage Effect Tensor M. The principal-valued Damage Effect Tensor is used to obtain the first scalar invariant of that Tensor and its inverse, which are employed in expressing and verifying the new proposed Damage Tensors. The study demonstrates that most of the new proposed Damage Tensors are verified within the framework of continuum Damage mechanics. In addition, new hybrid Damage Tensors are proposed which are defined in terms of the Damage Effect Tensor and the new proposed Damage Tensors. The new hybrid Damage Tensors are eventually expressed in terms of the Damage Effect Tensor.
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Chapter 11 – Symmetrization of the Effective stress Tensor
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Publisher Summary The aim of this chapter is to provide a solid mathematical basis for symmetrization methods of the Effective stress Tensor, and justification for their use and validity. The Effective stress Tensor is examined within the framework of continuum Damage mechanics. For a general state of deformation and Damage, it is seen that the Effective stress Tensor is usually not symmetric. Therefore, its symmetrization is necessary for a continuum theory to be valid. There are three types of symmetrization methods: explicit symmetrization, square root symmetrization, and implicit symmetrization. These three symmetrization methods are compared, and certain recommendations are made regarding their suitability. This chapter concludes that the explicit method produces higher Damage Effect values, thus resulting in higher Effective stresses than the other two methods. The implicit method produces the lowest symmetrized stress values. All three symmetrization methods display qualitatively the same variation of the Damage Effect Tensor. Only the explicit and implicit symmetrization methods depict more accurately the physics of the material Damage behavior.
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Chapter 16 – The kinematics of Damage for finite-strain elasto-plastic solids
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Publisher Summary This chapter introduces the kinematics of Damage for finite strain elasto-plastic deformation by using the fourth-order Damage Effect Tensor through the concept of the Effective stress within the framework of continuum Damage mechanics. This proposed approach provides a general description of kinematics of Damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field. The Damage is described kinematically in both the elastic domain and plastic domain using the fourth-order Damage Effect Tensor. This chapter characterizes the Damage Effect Tensor explicitly in terms of a kinematic measure of Damage through a second-order Damage Tensor. The finite elasto-plastic deformation behavior with Damage is also viewed within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation, the strain due to Damage and the associated dissipation energy due to this strain are introduced separately in the chapter.
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Chapter 8 – Metal matrix composites—Local approach
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:This chapter deals with a local approach to metal–matrix composites. The approach followed in this chapter to characterize Damage is termed local in the sense that Damage is introduced at the constituent or local level. For composite material, two Damage Tensors M M and M F are introduced for the two constituents, that is, matrix and fibers of the composite system. For a composite system consisting of n constituents, n Damage Tensors M (1) , M (2) ,…. , M ( n ) are introduced to locally characterize Damage in a complete manner. These Damage variables are then combined in a systematic way with an appropriate micromechemical constitutive model to develop the overall Damage response of the composite system. The matrix Damage Effect Tensor M M is assumed to reflect all types of Damage that the matrix material undergoes, like nucleation and coalescence of voids and mircocracks, whereas the fiber Damage Effect Tensor M F is considered to reflect all types of fiber Damage, like fracture of fibers. These two Tensors are then related through an overall Damage Effect Tensor M for the whole composite system.
George Z. Voyiadjis - One of the best experts on this subject based on the ideXlab platform.
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Some Basic Issues of Isotropic and Anisotropic Continuum Damage Mechanics
Handbook of Damage Mechanics, 2021Co-Authors: George Z. Voyiadjis, Peter I. Kattan, Mohammed A. YousefAbstract:This chapter includes two main topics in isotropic and anisotropic Damage mechanics. In the first topic, various new proposed Damage variables are introduced, examined, and compared. The scalar case pertaining to isotropic Damage is investigated, and several types of new Damage variables are proposed. The Damage variables introduced in this part can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. Moreover, higher-order strain energy forms are proposed. These higher-order strain energy forms along with some of the proposed Damage variables are used in trying to lay the theoretical groundwork for the design of unDamageable materials, i.e., materials that cannot be Damaged where the value of the Damage variable remains zero throughout the deformation process.The second topic presents a new concept of anisotropic Damage that is examined within the framework of continuum Damage mechanics. New proposed Damage Tensors are studied in order to investigate the Damage Effect variables in the mechanical behavior of materials. In addition, new hybrid Damage Tensors are proposed and defined in terms of the Damage Effect Tensor and the new proposed Damage Tensors. Accordingly, this study demonstrates that most of the new proposed Damage Tensors are verified within the framework of continuum Damage mechanics.
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new Tensors for anisotropic Damage in continuum Damage mechanics
Journal of Engineering Materials and Technology-transactions of The Asme, 2012Co-Authors: George Z. Voyiadjis, Mohammed A. Yousef, Peter I. KattanAbstract:In this work, new proposed Damage Tensors are studied in order to investigate the Damage Effect variables in the mechanical behavior of materials. All cases studied in this work are defined in terms of the elasticity of the material and based on the hypotheses of both elastic strain equivalence and elastic energy equivalence. Moreover, the new proposed Damage Tensors are anisotropically expressed in terms of the well-known Damage Effect Tensor M. The principal-valued Damage Effect Tensor is used to obtain the first scalar invariant of that Tensor and its inverse, which are employed in expressing and verifying the new proposed Damage Tensors. The study demonstrates that most of the new proposed Damage Tensors are verified within the framework of continuum Damage mechanics. In addition, new hybrid Damage Tensors are proposed which are defined in terms of the Damage Effect Tensor and the new proposed Damage Tensors. The new hybrid Damage Tensors are eventually expressed in terms of the Damage Effect Tensor.
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Chapter 11 – Symmetrization of the Effective stress Tensor
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Publisher Summary The aim of this chapter is to provide a solid mathematical basis for symmetrization methods of the Effective stress Tensor, and justification for their use and validity. The Effective stress Tensor is examined within the framework of continuum Damage mechanics. For a general state of deformation and Damage, it is seen that the Effective stress Tensor is usually not symmetric. Therefore, its symmetrization is necessary for a continuum theory to be valid. There are three types of symmetrization methods: explicit symmetrization, square root symmetrization, and implicit symmetrization. These three symmetrization methods are compared, and certain recommendations are made regarding their suitability. This chapter concludes that the explicit method produces higher Damage Effect values, thus resulting in higher Effective stresses than the other two methods. The implicit method produces the lowest symmetrized stress values. All three symmetrization methods display qualitatively the same variation of the Damage Effect Tensor. Only the explicit and implicit symmetrization methods depict more accurately the physics of the material Damage behavior.
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Chapter 16 – The kinematics of Damage for finite-strain elasto-plastic solids
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:Publisher Summary This chapter introduces the kinematics of Damage for finite strain elasto-plastic deformation by using the fourth-order Damage Effect Tensor through the concept of the Effective stress within the framework of continuum Damage mechanics. This proposed approach provides a general description of kinematics of Damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field. The Damage is described kinematically in both the elastic domain and plastic domain using the fourth-order Damage Effect Tensor. This chapter characterizes the Damage Effect Tensor explicitly in terms of a kinematic measure of Damage through a second-order Damage Tensor. The finite elasto-plastic deformation behavior with Damage is also viewed within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation, the strain due to Damage and the associated dissipation energy due to this strain are introduced separately in the chapter.
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Chapter 8 – Metal matrix composites—Local approach
Advances in Damage Mechanics, 2006Co-Authors: George Z. Voyiadjis, Peter I. KattanAbstract:This chapter deals with a local approach to metal–matrix composites. The approach followed in this chapter to characterize Damage is termed local in the sense that Damage is introduced at the constituent or local level. For composite material, two Damage Tensors M M and M F are introduced for the two constituents, that is, matrix and fibers of the composite system. For a composite system consisting of n constituents, n Damage Tensors M (1) , M (2) ,…. , M ( n ) are introduced to locally characterize Damage in a complete manner. These Damage variables are then combined in a systematic way with an appropriate micromechemical constitutive model to develop the overall Damage response of the composite system. The matrix Damage Effect Tensor M M is assumed to reflect all types of Damage that the matrix material undergoes, like nucleation and coalescence of voids and mircocracks, whereas the fiber Damage Effect Tensor M F is considered to reflect all types of fiber Damage, like fracture of fibers. These two Tensors are then related through an overall Damage Effect Tensor M for the whole composite system.
Taehyo Park - One of the best experts on this subject based on the ideXlab platform.
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The kinematics of Damage for finite-strain elasto-plastic solids
International Journal of Engineering Science, 1999Co-Authors: George Z. Voyiadjis, Taehyo ParkAbstract:In this paper the kinematics of Damage for finite strain, elasto-plastic deformation is introduced using the fourth-order Damage Effect Tensor through the concept of the Effective stress within the framework of continuum Damage mechanics. In the absence of the kinematic description of Damage deformation leads one to adopt one of the following two different hypotheses for the small deformation problems. One uses either the hypothesis of strain equivalence or the hyphothesis of energy equivalence in order to characterize the Damage of the material. The proposed approach in this work provides a general description of kinematics of Damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. In this work, the Damage is described kinematically in both the elastic domain and plastic domain using the fourth order Damage Effect Tensor which is a function of the second-order Damage Tensor. The Damage Effect Tensor is explicitly characterized in terms of a kinematic measure of Damage through a second-order Damage Tensor. Two kinds of second-order Damage Tensor representations are used in this work with respect to two reference configurations. The finite elasto-plastic deformation behavior with Damage is also viewed here within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation one introduces seperately the strain due to Damage and the associated dissipation energy due to this strain.
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Kinematic Description of Damage
Journal of Applied Mechanics, 1998Co-Authors: Taehyo Park, George Z. VoyiadjisAbstract:In this paper the kinematics of Damage for finite elastic deformations is introduced using the fourth-order Damage Effect Tensor through the concept of the Effective stress within the framework of continuum Damage mechanics. However, the absence of the kinematic description of Damage deformation leads one to adopt one of the following two different hypotheses. One uses either the hypothesis of strain equivalence or the hypothesis of energy equivalence in order to characterize the Damage of the material. The proposed approach in this work provides a relation between the Effective strain and the Damage elastic strain that is also applicable to finite strains. This is accomplished in this work by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. The proposed approach shows that it is equivalent to the hypothesis of energy equivalence for finite strains. In this work, the Damage is described kinematically in the elastic domain using the fourth-order Damage Effect Tensor which is a function of the second-order Damage Tensor. The Damage Effect Tensor is explicitly characterized in terms of a kinematic measure ofDamage through a second-order Damage Tensor. The constitutive equations of the elastic-Damage behavior are derived through the kinematics of Damage using the simple mapping instead of the other two hypotheses.
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Kinematics of large elastoplastic Damage deformation
Damage Mechanics in Engineering Materials, 1998Co-Authors: George Z. Voyiadjis, Taehyo ParkAbstract:Abstract In this paper the kinematics of Damage for finite strain, elasto-plastic deformation is introduced using the fourth-order Damage Effect Tensor through the concept of the Effective stress within the framework of continuum Damage mechanics. In the absence of the kinematic description of Damage deformation leads one to adopt one of the following two different hypotheses for the small deformation problems. One uses either the hypothesis of strain equivalence or the hyphothesis of energy equivalence in order to characterize the Damage of the material. The proposed approach in this work provides a general description of kinematics of Damage applicable to finite strains. This is accomplished by directly considering the kinematics of the deformation field and furthermore it is not confined to small strains as in the case of the strain equivalence or the strain energy equivalence approaches. In this work, the Damage is described kinematically in both the elastic domain and plastic domain using the fourth order Damage Effect Tensor which is a function of the second-order Damage Tensor. The Damage Effect Tensor is explicitly characterized in terms of a kinematic measure of Damage through a second-order Damage Tensor. Two kinds of second-order Damage Tensor representations are used in this work with respect to two reference configurations. The finite elasto-plastic deformation behavior with Damage is also viewed here within the framework of thermodynamics with internal state variables. Using the consistent thermodynamic formulation one introduces seperately the strain due to Damage and the associated dissipation energy due to this strain.
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Anisotropic Damage Effect Tensors for the Symmetrization of the Effective Stress Tensor
Journal of Applied Mechanics, 1997Co-Authors: George Z. Voyiadjis, Taehyo ParkAbstract:Based on the concept of the Effective stress and on the description of anisotropic Damage deformation within the framework of continuum Damage mechanics, a fourth order Damage Effective Tensor is properly defined. For a general state of deformation and Damage, it is seen that the Effective stress Tensor is usually asymmetric. Its symmetrization is necessary for a continuum theory to be valid in the classical sense. In order to transform the current stress Tensor to a symmetric Effective stress Tensor, a fourth order Damage Effect Tensor should be defined such that it follows the rules of Tensor algebra and maintains a physical description of Damage. Moreover, an explicit expression of the Damage Effect Tensor is of particular importance in order to obtain the constitutive relation in the Damaged material. The Damage Effect Tensor in this work is explicitly characterized in terms of kinematic measure of Damage through a second-order Damage Tensor. In this work, Tensorial forms are used for the derivation of such a linear transformation Tensor which is then converted to a matrix form.
C L Chow - One of the best experts on this subject based on the ideXlab platform.
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Damage mechanics characterization on the fatigue behaviour of a solder joint material
Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2001Co-Authors: C L Chow, Fan Yang, H.e. FangAbstract:This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic Damage considerations. A separate report will be made to present a comprehensive Damage model describing life prediction of the solder material under thermomechanical fatigue loading. The method is based on a theory of Damage mechanics which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A Damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behavior of a typical solder material. With the introduction of a Damage Effect Tensor, the constitutive equations are derived to enable the formulation of a fatigue Damage dissipative potential function and a fatigue Damage criterion. The fatigue evolution is subsequently developed based on the hypothesis that the overall Damage is induced by the accumulation of fatigue and plastic Damage. This Damage mechanics approach offers a systematic and versatile means that is Effective in modeling the entire process of material failure ranging from Damage initiation and propagation leading eventually tomore » macro-crack initiation and growth. As the model takes into account the load history Effect and the interaction between plasticity Damage and fatigue Damage, with the aid of a modified general purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.« less
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A Damage-Coupled TMF Constitutive Model for Solder Alloy
International Journal of Damage Mechanics, 2001Co-Authors: Yong Wei, C L ChowAbstract:This paper presents the development of a Damage-coupled constitutive model to characterize the mechanical behavior of 63Sn-37Pb solder material under thermo-mechanical fatigue (TMF) loading. Based on the theory of Damage mechanics, two internal state variables, known as the Damage parameters, are introduced to characterize material degradation due to the change of material microstructures under load. Then, a Damage Effect Tensor is proposed to define the Effective stress for a Damaged material. In general, there are two different kinds of Damage accumulation depending upon the mode of loading: inelastic Damage and fatigue Damage. With the aid of irreversible thermodynamics, the Damage evolution equations are established. A failure criterion is proposed based on the equivalent Damage accumulation in materials. A test program to determine the material parameters is also presented.The Damage model is implemented in a finite element program ABAQUS through its user-defined material subroutine UMAT. The model i...
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Damage mechanics characterization on fatigue behavior of a solder joint material
1998Co-Authors: C L Chow, Fan Yang, H.e. FangAbstract:This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic Damage considerations. A separate report will be made to present a comprehensive Damage model describing life prediction of the solder material under thermomechanical fatigue loading. The method is based on a theory of Damage mechanics which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A Damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behavior of a typical solder material. With the introduction of a Damage Effect Tensor, the constitutive equations are derived to enable the formulation of a fatigue Damage dissipative potential function and a fatigue Damage criterion. The fatigue evolution is subsequently developed based on the hypothesis that the overall Damage is induced by the accumulation of fatigue and plastic Damage. This Damage mechanics approach offers a systematic and versatile means that is Effective in modeling the entire process of material failure ranging from Damage initiation and propagation leading eventually to macro-crack initiation and growth. As the model takes into account the load history Effect and the interaction between plasticity Damage and fatigue Damage, with the aid of a modified general purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.
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A Method of Damage Mechanics Analysis for Solder Material
Key Engineering Materials, 1997Co-Authors: H.e. Fang, C L Chow, Fan YangAbstract:This paper presents as a method of Damage mechanics analysis for solder joint material stressed to extensive plastic deformation. The material chosen for the current work is the 60Sn-40Pb eutectic alloy due to its wide use. The analysis is based on the thermodynamic theory of irreversible processes. With the introduction of a set of internal state variables, known as Damage variables, and a Damage Effect Tensor, a Damage dissipative potential function is proposed to enable the formulation of the constitutive equations of elasticity and plasticity coupled with Damage. The equations of Damage evolution are also derived to monitor Damage initiation and growth. Before a Damage analysis can be performed with a finite element analysis, the mechanical properties of the chosen solder joint material and its Damage variables must first be determined. A method of experimental analysis was developed and used to successfully measure the highly strain sensitive 60Sn-40Pb solder material. The measured properties are presented and various characteristics of the solder material are examined and discussed. 7 refs., 8 figs.
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On Damage Strain Energy Release Rate Y
International Journal of Damage Mechanics, 1995Co-Authors: X. F. Chen, C L ChowAbstract:In the application of the theory of Damage mechanics to solve a wide range of practical engineering problems, a generalized formulation of Damage strain energy release rate Y is required. This is because the Damage strain energy release rate Y, which is the thermodynamic conjugate force of Damage variable D, is used to derive Damage evolution equation. For the case of isotropic Damage, the Damage variable is degenerated to a scalar. Accordingly, the derivation of the Damage strain energy release rate is relatively straightforward. However, it is much more involved in the case of anisotropic Damage. Currently, no such generalized form of the Damage strain energy release rate is available. This paper is intended to present the development of three formulations of Damage strain energy release rate based on three different forms of the Damage Effect Tensor M(D) for which D is a second order symmetric Tensor. The realization of the anisotropic Damage strain energy rate formulations makes it possible to obtain ...
H.e. Fang - One of the best experts on this subject based on the ideXlab platform.
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Damage mechanics characterization on the fatigue behaviour of a solder joint material
Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2001Co-Authors: C L Chow, Fan Yang, H.e. FangAbstract:This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic Damage considerations. A separate report will be made to present a comprehensive Damage model describing life prediction of the solder material under thermomechanical fatigue loading. The method is based on a theory of Damage mechanics which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A Damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behavior of a typical solder material. With the introduction of a Damage Effect Tensor, the constitutive equations are derived to enable the formulation of a fatigue Damage dissipative potential function and a fatigue Damage criterion. The fatigue evolution is subsequently developed based on the hypothesis that the overall Damage is induced by the accumulation of fatigue and plastic Damage. This Damage mechanics approach offers a systematic and versatile means that is Effective in modeling the entire process of material failure ranging from Damage initiation and propagation leading eventually tomore » macro-crack initiation and growth. As the model takes into account the load history Effect and the interaction between plasticity Damage and fatigue Damage, with the aid of a modified general purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.« less
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Damage mechanics characterization on fatigue behavior of a solder joint material
1998Co-Authors: C L Chow, Fan Yang, H.e. FangAbstract:This paper presents the first part of a comprehensive mechanics approach capable of predicting the integrity and reliability of solder joint material under fatigue loading without viscoplastic Damage considerations. A separate report will be made to present a comprehensive Damage model describing life prediction of the solder material under thermomechanical fatigue loading. The method is based on a theory of Damage mechanics which makes possible a macroscopic description of the successive material deterioration caused by the presence of microcracks/voids in engineering materials. A Damage mechanics model based on the thermodynamic theory of irreversible processes with internal state variables is proposed and used to provide a unified approach in characterizing the cyclic behavior of a typical solder material. With the introduction of a Damage Effect Tensor, the constitutive equations are derived to enable the formulation of a fatigue Damage dissipative potential function and a fatigue Damage criterion. The fatigue evolution is subsequently developed based on the hypothesis that the overall Damage is induced by the accumulation of fatigue and plastic Damage. This Damage mechanics approach offers a systematic and versatile means that is Effective in modeling the entire process of material failure ranging from Damage initiation and propagation leading eventually to macro-crack initiation and growth. As the model takes into account the load history Effect and the interaction between plasticity Damage and fatigue Damage, with the aid of a modified general purpose finite element program, the method can readily be applied to estimate the fatigue life of solder joints under different loading conditions.
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A Method of Damage Mechanics Analysis for Solder Material
Key Engineering Materials, 1997Co-Authors: H.e. Fang, C L Chow, Fan YangAbstract:This paper presents as a method of Damage mechanics analysis for solder joint material stressed to extensive plastic deformation. The material chosen for the current work is the 60Sn-40Pb eutectic alloy due to its wide use. The analysis is based on the thermodynamic theory of irreversible processes. With the introduction of a set of internal state variables, known as Damage variables, and a Damage Effect Tensor, a Damage dissipative potential function is proposed to enable the formulation of the constitutive equations of elasticity and plasticity coupled with Damage. The equations of Damage evolution are also derived to monitor Damage initiation and growth. Before a Damage analysis can be performed with a finite element analysis, the mechanical properties of the chosen solder joint material and its Damage variables must first be determined. A method of experimental analysis was developed and used to successfully measure the highly strain sensitive 60Sn-40Pb solder material. The measured properties are presented and various characteristics of the solder material are examined and discussed. 7 refs., 8 figs.
