A Mechanical Fatigue Damage Evolution Model for PB-Free Solder Materials

2008 ◽  
Author(s):  
Leila J. Ladani ◽  
Jafar Razmi
Keyword(s):  
Damage Evolution ◽  
Pure Shear ◽  
Damage Model ◽  
Energy Partitioning ◽  
Evolution Model ◽  
Ductile Material ◽  
Anisotropic Damage ◽  
Mechanical Fatigue ◽  
The Subject ◽  
Free Solder

Evaluating state of damage in a ductile material as it experiences mechanical fatigue and cyclic loading poses much complexity and has been the subject of many researches. This study revisits the anisotropic damage model developed by Lemaitre (1992) and proposes to use his model combined with a micro-mechanics and mechanism based damage evolution model (Energy Partitioning Damage Evolution (EPDE)) and also a Unified Creep Plasticity-based model to predict the state of damage. The model is examined for pure shear and is applied to Pb-free solder materials. New anisotropic damage model exponents are generated using experimental data for Pb-free solder for both EPDE and UPC-based models and are compared with exponents generated previously under the assumption of isotropic and homogenous damage evolution.

Failure Predictions for DP Steel Cross-die Test using Anisotropic Damage

2011 ◽  
Vol 21 (5) ◽  
pp. 713-754 ◽  
Author(s):  
M. S. Niazi ◽  
H. H. Wisselink ◽  
T. Meinders ◽  
J. Huétink
Keyword(s):  
Strain Rate ◽  
Damage Evolution ◽  
Damage Model ◽  
Anisotropic Damage ◽  
Continuum Damage ◽  
Anisotropic Plasticity ◽  
Continuum Damage Model ◽  
Damage Models ◽  
Isotropic Damage ◽  
Failure Predictions

The Lemaitre's continuum damage model is well known in the field of damage mechanics. The anisotropic damage model given by Lemaitre is relatively simple, applicable to nonproportional loads and uses only four damage parameters. The hypothesis of strain equivalence is used to map the effective stress to the nominal stress. Both the isotropic and anisotropic damage models from Lemaitre are implemented in an in-house implicit finite element code. The damage model is coupled with an elasto-plastic material model using anisotropic plasticity (Hill-48 yield criterion) and strain-rate dependent isotropic hardening. The Lemaitre continuum damage model is based on the small strain assumption; therefore, the model is implemented in an incremental co-rotational framework to make it applicable for large strains. The damage dissipation potential was slightly adapted to incorporate a different damage evolution behavior under compression and tension. A tensile test and a low-cycle fatigue test were used to determine the damage parameters. The damage evolution was modified to incorporate strain rate sensitivity by making two of the damage parameters a function of strain rate. The model is applied to predict failure in a cross-die deep drawing process, which is well known for having a wide variety of strains and strain path changes. The failure predictions obtained from the anisotropic damage models are in good agreement with the experimental results, whereas the predictions obtained from the isotropic damage model are slightly conservative. The anisotropic damage model predicts the crack direction more accurately compared to the predictions based on principal stress directions using the isotropic damage model. The set of damage parameters, determined in a uniaxial condition, gives a good failure prediction under other triaxiality conditions.

scholarly journals A Strain Rate-Dependent Damage Evolution Model for Concrete Based on Experimental Results

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Bin Xu ◽  
Xiaoyan Lei ◽  
P. Wang ◽  
Hui Song
Keyword(s):  
Strain Rate ◽  
Uniaxial Compression ◽  
Damage Evolution ◽  
Damage Model ◽  
Evolution Model ◽  
Experimental Results ◽  
Strain Rates ◽  
Compression Tests ◽  
Stress Strain ◽  
Actual Damage

There are various definitions of damage variables from the existing damage models. The calculated damage value by the current methods still could not well correspond to the actual damage value. Therefore, it is necessary to establish a damage evolution model corresponding to the actual damage evolution. In this paper, a strain rate-sensitive isotropic damage model for plain concrete is proposed to describe its nonlinear behavior. Cyclic uniaxial compression tests were conducted on concrete samples at three strain rates of 10−3s−1, 10−4s−1, and 10−5s−1, respectively, and ultrasonic wave measurements were made at specified strain values during the loading progress. A damage variable was defined using the secant and initial moduli, and concrete damage evolution was then studied using the experimental results of the cyclic uniaxial compression tests conducted at the different strain rates. A viscoelastic stress-strain relationship, which considered the proposed damage evolution model, was presented according to the principles of irreversible thermodynamics. The model results agreed well with the experiment and indicated that the proposed damage evolution model can accurately characterize the development of macroscopic mechanical weakening of concrete. A damage-coupled viscoelastic constitutive relationship of concrete was recommended. It was concluded that the model could not only characterize the stress-strain response of materials under one-dimensional compressive load but also truly reflect the degradation law of the macromechanical properties of materials. The proposed damage model will advance the understanding of the failure process of concrete materials.

Partitioned Cyclic Fatigue Damage Evolution Model for PB-Free Solder Materials

2007 ◽  
Author(s):  
Leila J. Ladani ◽  
A. Dasgupta
Keyword(s):  
Fatigue Damage ◽  
Creep Deformation ◽  
Damage Evolution ◽  
Evolution Model ◽  
Micro Scale ◽  
Elastic Plastic ◽  
Constitutive Properties ◽  
Free Solder ◽  
Cyclic Damage ◽  
Creep Deformations

This study presents an approach to predict the degree of material degradation and the resulting changes in constitutive properties during cyclic loading in viscoplastic materials in micro-scale applications. The objective in the modeling approach is to address the initiation and growth of distributed micro-damage, in the form of micro-cracks and micro-voids, as a result of cyclic, plastic and creep deformations of material. This study extends an existing micromechanics-based approach, developed for unified viscoplastic models [Wen, et al, 2001], which uses dislocation mechanics to predict damage due to distributed micro-scale fatigue crack initiation [Mura and Nakasone, 1990]. In the present study, the approach is extended to a partitioned viscoplastic framework, because the micro-scale mechanisms of deformation and damage are different for plastic and creep deformation. In this approach, the model constants for estimating cyclic damage evolution are allowed to be different for creep and plastic deformations. A partitioned viscoplastic constitutive model is coupled with an energy partitioning (E-P) damage model [Oyan and Dasgupta, 1992] to assess fatigue damage evolution due to cyclic elastic, plastic and creep deformations. Wen’s damage evolution model is extended to include damage evolution due to both plastic and creep deformations. The resulting progressive degradation of elastic, plastic and creep constitutive properties are continuously assessed and updated. The approach is implemented on a viscoplastic Pb-free solder. Dominant deformation modes in this material are dislocation slip for plasticity and diffusion-assisted dislocation climb/glide for creep. The material’s behavior shows a good correlation with the proposed damage evolution model. Damage evolution constants for plastic and creep deformation were obtained for this Pb-free solder from load drop data collected from the mechanical cycling experiments at different temperatures. The amount of cyclic damage is evaluated and compared with experiment.

On the Dependency of Ductile Damage Evolution to Stress State with Shock Loading Pre-Mechanical Working in 7075-T6 Aluminum Alloy

2016 ◽  
Vol 08 (04) ◽  
pp. 1650050 ◽  
Author(s):  
Sina Gohari Rad ◽  
Majid Alitavoli ◽  
Asghar Zajkani ◽  
Abolfazl Darvizeh
Keyword(s):  
Aluminum Alloy ◽  
Stress State ◽  
Damage Evolution ◽  
Damage Model ◽  
Evolution Model ◽  
Pressure Effects ◽  
Ductile Damage ◽  
Plastic Behavior ◽  
Special Focus ◽  
Mechanical Working

In this paper, the evolution of a ductile damage in the 7075-T6 aluminum alloy is considered based on stress state parameters with a special focus on pre-mechanical working dependency. Uniaxial stress–strain curves are investigated experimentally for two conditions; specimens with shock loaded pre-mechanical working and without it. This kind of loading is applied in order to find out impulsive pressure effects of damage variation procedure. Some experiments are done to take different stress states. Applying two fracture initiations criteria, i.e., Hosford–Coulomb and Xue models, two types of fracture locus of Al-7075-T6 are predicted in terms of plastic strains and stress state parameters under above conditions. By considering experimental data, a new ductile damage evolution model is proposed among plastic behavior. It is introduced by explicating an uncoupled plasticity and related to initial rate dependent stress state. By using both fracture models, our damage evolution model is implemented, phenomenologically as well as the Xue damage model, to compare results.

Influence of Ductile Damage Evolution on the Collapse Load of Frames

2010 ◽  
Vol 77 (3) ◽  
Author(s):  
Edwin L. Chica ◽  
Antolín L. Ibán ◽  
José M. G. Terán ◽  
Pablo M. López-Reyes
Keyword(s):  
Ductile Fracture ◽  
Damage Evolution ◽  
Damage Model ◽  
Ductile Failure ◽  
Ductile Material ◽  
Collapse Load ◽  
Local Criterion ◽  
Solid Materials ◽  
Damage Models ◽  
Isotropic Damage

In this note we analyze the influence of four damage models on the collapse load of a structure. The models considered here have been developed using the hypothesis based on the concept of effective stress and the principle of strain equivalence and they were proposed by Lemaitre and Chaboche (1990, Mechanics of Solid Materials), Wang (1992, “Unified CDM Model and Local Criterion for Ductile Fracture—I. Unified CDM Model for Ductile Fracture,” Eng. Fract. Mech., 42, pp. 177–183), Chandrakanth and Pandey (1995, “An Isotropic Damage Model for Ductile Material,” Eng. Fract. Mech., 50, pp. 457–465), and Bonora (1997, “A Nonlinear CDM Model for Ductile Failure,” Eng. Fract. Mech., 58, pp. 11–28). The differences between them consist mainly in the form of the dissipative potential from which the kinetic law of damage is derived and also in the assumptions made about some parameters of the material.

Mesoscopic Thermal-Mechanical Fire Damage Modeling of High Performance Concrete

2011 ◽  
Vol 194-196 ◽  
pp. 1095-1098
Author(s):  
Jie Zhao ◽  
Jian Jun Zheng ◽  
Gai Fei Peng ◽  
Klaas van Breugel
Keyword(s):  
Moisture Transport ◽  
Damage Evolution ◽  
High Performance ◽  
High Performance Concrete ◽  
Damage Model ◽  
Damage Mechanism ◽  
Mechanical Degradation ◽  
Anisotropic Damage ◽  
Fire Damage ◽  
Material Degradation

High performance concrete will undergo thermal-mechanical degradation or even spalling under high temperature conditions, such as fire, and the safety of concrete structures will be endangered. To prevent concrete from fire damage, the damage mechanism should be thoroughly understood. In this paper, an anisotropic damage model is presented to analyze the thermal-mechanical degradation of concrete. The vapor pressure and the moisture transport are taken into account. The damage evolution history can be traced with the temperature propagation and the degree of material degradation can be predicted through the model.

Parameter estimation of an anisotropic damage model for concrete using genetic algorithms

2015 ◽  
Vol 26 (6) ◽  
pp. 801-825 ◽  
Author(s):  
Muhammad A Wardeh ◽  
Houssam A Toutanji
Keyword(s):  
Damage Evolution ◽  
Elastic Strain ◽  
Strain Energy ◽  
Damage Mechanics ◽  
Evolution Equations ◽  
Damage Model ◽  
Elastic Strain Energy ◽  
Constitutive Law ◽  
Anisotropic Damage ◽  
Unknown Parameters

This article presents an anisotropic damage model for concrete that couples between elasticity and continuum damage mechanics. The formulation of constitutive model is based on the elastic strain energy in the framework of irreversible thermodynamics. The thermodynamic free energy is represented as a scalar function of elastic strain and damage tensors and used to derive the constitutive law and thermodynamic conjugate force of damage that is used to derive the dissipation potential. The damage evolution law is governed by the normality rule. The formulation of elastic strain energy of damaged material is capable of modeling the concrete anisotropic behavior under different loadings without decoupling the stress or damage release rate. A series of unknown parameters in the model formulation was used to control the constitutive behavior and damage surface. A Genetic algorithm FORTRAN subroutine is used to estimate these parameters based on the coupling between the constitutive and damage evolution equations. The performance of the damage model is verified with the experimental data from the literature. The model has shown a good agreement with the experimental results. It describes the anisotropy induced by the crack development within the concrete.

scholarly journals The effect of plasticity on damage evolution using a relaxation-based material model

2018 ◽  
Vol 27 (5-6) ◽  
Author(s):  
Stephan Schwarz ◽  
Klaus Hackl ◽  
Philipp Junker
Keyword(s):  
Damage Evolution ◽  
Pure Shear ◽  
Matrix Material ◽  
Damage Model ◽  
Material Model ◽  
Realistic Model ◽  
Isotropic Hardening ◽  
Viscous Effects ◽  
Loading Rates ◽  
Rate Dependent

AbstractAs damage occurs in the context of high stresses that are also related to the presence of plastic strains, it is natural to investigate the effect of plasticity on damage evolution and to thus achieve a more realistic model. In this work, the existing and new damage model presented in [Junker P, Schwarz S, Makowski J, Hackl K. Continuum Mech. Therm. 2017, 29 (1), 291–310] is enhanced with plasticity and isotropic hardening. The damage model is based on a relaxation-based approach and does not require additional complex regularization techniques besides considering viscous effects. The benefit of the model are mesh-independent results for the rate-dependent case, even without considering, e.g. gradient terms for mathematical regularization. The enhancement with plasticity and isotropic hardening was investigated for a representative volume element that considerd a damaging matrix material and non-damaging hard precipitates. Two different loading types, pure tension and pure shear, yielded the homogenized stress/strain response for the material at various loading rates. Hereto, several finite discretizations in terms of finite-element meshes were used. The results underline the mesh-independence for physically reasonable loading rates and viscosities.

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