Nonlinear Continuum Damage Mechanics Model Research Articles

Constitutive and damage model for the whole-life uniaxial ratcheting behavior of SAC305

With the wide application of SAC305 solders in electronic packaging, it is important to examine their reliability. In this study, uniaxial ratcheting experiments were carried out on SAC305 solders with varying loading rates, mean stresses, and stress amplitudes at room temperature. Based on the unified creep–plasticity constitutive model applicable to SAC305 solders, a nonlinear continuum damage mechanics model was established to simulate the whole-life ratcheting behavior. The damage variable was extracted from the elastic modulus decline of the unloading section during the cyclic loading process, and its evolution was based on the damage dissipation potential, which was derived from the theory of continuum damage mechanics. In addition, the normalized life was used to correct the evolution of the damage variable. For a more accurate description of their evolution, the energy method was used to modify the damage evolution parameters under different loading conditions. Finally, the uniaxial ratcheting behavior of SAC305 solder could be accurately described by the modified damage-coupled constitutive model under different loading conditions.

A meshless approach to non-local damage modelling of concrete

A non-linear continuum damage mechanics model for concrete constructions is analysed using a radial point interpolation meshless method (RPIM). The fundamental mathematical relations and the material model are fully characterized. The 2D plane stress RPIM formulation is extended to a rate-independent standard (local) damage model considering both tension and compression static states. Additionally, in this work, the local damage formulation is modified considering a non-local constitutive damage criterion with regard to a Helmholtz free energy potential. Here, the internal variational fields, such as local and non-local damage variables, are determined by a return-mapping damage algorithm. Due to the non-linear nature of the phenomenon, a displacement controlled Newton-Raphson iterative approach is adopted to attain the non-linear damage solution. In the end, the performance of the proposed non-local damage model is evaluated using an experimental test of a notched-three-point bending beam available in the literature. The obtained solution shows that the meshless methods are capable to effectively analyse concrete structures assuming a non-linear non-local continuum damage model.

A continuum damage mechanics-based unified creep and plasticity model for solder materials

A nonlinear continuum damage mechanics model is developed for both lead-rich and lead-free solder materials. A unified creep–plasticity constitutive relationship is adopted to simulate the inelastic behaviors; both isotropic and nonlinear kinematic hardening are considered. A traditional continuum damage evolution law is a function of actual damage parameter and effective accumulated plastic strain. In the current work, absolute temperature is introduced into the damage model to reflect the effect of temperature on the accumulated damage mechanism. The mechanical properties of solders, incorporating damage initiation and accumulation, were analyzed based on the model developed. Fatigue life under fully reversed cycling is investigated by monitoring the change in peak stresses, which decreases continuously, owing to damage accumulation. The numerical results were compared with experimental data. It was shown that the developed model can predict the whole damage accumulation process of different solder materials with reasonable accuracy.

Fatigue life prediction of notched components based on a new nonlinear continuum damage mechanics model

A CDM (continuum damage mechanics) model for damage evaluation is here considered and applied to the study of two different typologies of notched and cylindrical specimens. The model presents some parameter and authors determined them in a previous work testing cylindrical and smooth specimens.Firstly fatigue characterization was conducted and the SN curves found. In order to evaluate the capability of CDM model to predict the sequence effect and to simulate a more realistic loading condition, tests with various loading blocks were carried on and in particular high-low, low-high and random blocks were applied to the three specimens considered. Model previsions showed good agreement with results for each geometry considered.

Fatigue life prediction under variable loading based on a new non-linear continuum damage mechanics model

This work presents a non-linear continuum damage mechanics model based on general thermodynamic framework developed by Lemaitre and Chaboche. The proposed model has been formulated to take into account the material damage evolution at different load levels and it allows the effect of the loading sequence to be included; by means of a recurrence formula derived for multilevel loading, complex load sequences can be considered. The fatigue test data for a hardened and tempered steel have been used to verify the model proposed in this paper and the results show a good agreement to predict fatigue life under complex load sequences.

A Continuum Damage Mechanics Model on Creep Rupture Life Assessment of a Steam Turbine Rotor

A nonlinear continuum damage mechanics model is proposed to assess the high temperature creep life of a steam turbine rotor, in which the effect of mean stress is taken into account and the damage is accumulated nonlinearly. The model is applied to a 300 MW steam turbine under hot start operation. The results are compared with those from the linear accumulation theory that is dominant in the creep life assessment of steam turbine rotors at present. The comparison results show that the nonlinear continuum damage mechanics model describes the accumulation and development of damage better than the linear accumulation theory.

Identification of the parameters of a non-linear continuum damage mechanics model for ductile failure in metals

Damage modelling in ductile metal has received a lot of attention in the last thirty years. Since 1969, many models have been proposed in the literature even though, in most of the cases, the experimental aspects related to the damage parameter evaluation have often been neglected. In this work the procedure to evaluate the damage parameters, for the continuum damage mechanics based model proposed by Bonora, is presented. Here, the ductile damage is experimentally measured in terms of progressive elastic modulus reduction as a function of strain measured in an hourglass-shaped specimen loaded in tension. The proposed technique, which is based on performing multiple, partial unloading, is reliable and relatively simple to implement. Additional tensile testing, performed with a round notch tensile bar, provides critical data that can be used to identify unequivocally the full damage parameter set and to assure their geometry transferability. The procedure presented here has been applied to identify the damage parameters for 20MnMoNi55 steel.

An effective continuum damage mechanics model for creep–fatigue life assessment of a steam turbine rotor

A nonlinear Continuum Damage Mechanics model is proposed to assess the creep–fatigue life of a steam turbine rotor, in which the effects of complex multiaxial stress and the coupling of fatigue and creep are taken into account. The nonlinear evolution of damage is also considered. The model is applied to a 600 MW steam turbine under a practical start–stop operation. The results are compared with those from the linear accumulation theory that is dominant in life assessment of steam turbine rotors at present. The comparison show that the nonlinear continuum damage mechanics model describes the accumulation and development of damage better than the linear accumulation theory.

Machining Simulation for Ceramics Based on Continuum Damage Mechanics

An abrasive machining process for ceramics is simulated with a nonlinear thermodynamic constitutive model based on the principle of continuum damage mechanics (CDM). The model consists of a set of parallel Maxwell-type elements arranged in series with a spring. It incorporates stochastic material microstructure through two sets of the newly introduced material parameters, spring-like constants Cr and damping-like coefficients arr=1,2,…,n. Damage is considered cumulative and related with current stress and damage state in a ceramic workpiece during loading, which constitutes damage evolution. A fourth-order isotropic damage tensor is introduced. This highly nonlinear CDM model is reduced to an incremental formulation and approximated by a 3D nonlinear finite element program based on the Newton-Raphson method. The stress-strain correlation calculated from the current model is presented for alumina, silicon carbide, and silicon nitride. The predicted results of damage versus the depth of cut for the three ceramics subjected to machining with single diamond grit are validated by the experiment. As one example, the development of damage with the movement of the abrasive grit in a silicon nitride workpiece is demonstrated by a contour plot. The final part of this paper presents the calculated distribution of residual stress in a silicon nitride sample and the factors contributing to the distribution are discussed.

A continuum damage mechanics model on low cycle fatigue life assessment of steam turbine rotor

A nonlinear Continuum Damage Mechanics model (CDM) is proposed to assess the low cycle fatigue life of a steam turbine rotor, in which the effects of mean stress are taken into account and the damage is accumulated nonlinearly. The model is applied to a 200 MW steam turbine under cold start and sliding parameter stop. The results are compared with those from the linear accumulation theory that is dominant in life assessment of steam turbine rotors at present. The comparison results show that the nonlinear CDM model describes the accumulation and development of damage better than the linear accumulation theory.

A nonlinear CDM model for ductile failure

Continuum Damage Mechanics (CDM) has bee proved to be a powerful tool in all those problems where it is difficult to use classical fracture mechanics concepts as a result of the following effects: effects of large-scale yielding plasticity (for instance, ductile rupture due to large deformations, geometry dependence of the J-resistance curve), three-dimensional effects, effects of multiple sites damage such as short cracks, multiple cracking in composites, and so on. In this paper, a new nonlinear CDM plasticity damage model is proposed. The model was developed on the experimental observations that the growth of microvoids results in a nonlinear damage accumulation with plastic deformation. Three basic possible damage evolution trends are identified and taken into account by a single damage model. The model proposed was applied successfully to seven different materials that clearly exhibit the three different damage evolution trends. The effects of triaxial state of stress on material damage parameters, such as the material strain to failure, are also discussed. Material damage constants and the procedure for their identification are presented.