Comparison of different finite deformation inelastic damage models within multiplicative elastoplasticity for ductile materials

The new contribution of this study is to formulate two wellknown isotropic elastoplastic damage concepts for ductile materials in the framework of geometrically exact finite multiplicative elastoplasticity. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. In contrast, the Gurson model takes into account the balance of mass separately to formulate damage evolution. In this contribution both formulations are based on logarithmic Hencky strains leading to a simple application of the so called exponential map stress integrator which is the algorithmic counterpart of the multiplicative elastoplastic formulation adopted. Special emphasis is directed towards the numerical implementation of these models within the framework of finite element analysis of inelastic boundary value problems. To compare the results of numerical computations several standard examples within finite elastoplasticity are analysed with both damage models and the results are contrasted to the outcome of an analysis with the classical v. Mises model. thereby, the dramatic influence of damage on the behaviour within necking and localization computations is highlighted. The different behaviour of the two models considered within compression dominated problems is appreciated.     

Mesh objective continuum damage models for ductile fracture

During machining processes, the work piece material is subjected to high deformation rates, increased temperature, large plastic deformations, damage evolution and fracture. In this context the Johnson‐Cook failure model is often used even though it exhibits pathological mesh size dependence. To remove the mesh size sensitivity, a set of mesh objective damage models is proposed based on a local continuum damage formulation combined with the concept of a scalar damage phase field. The first model represents a mesh objective augmentation of the well‐established element removal model, whereas the second one degrades the continuum stress in a smooth fashion. Plane strain plate and hat specimens are used in the finite element simulations, with the restriction to the temperature and rate independent cases. To investigate the influence of mesh distortion, a structured and an unstructured meshes were used for the respective specimen. For structured meshes, the results clearly show that the pathological mesh size sensitivity is removed for both models. When considering unstructured meshes, the mesh size sensitivity is more complex as revealed by the considered hat‐specimen shear test. Nevertheless, the present work indicates that the proposed models can predict realistic ductile failure behaviors in a mesh objective fashion. Copyright © 2015 John Wiley & Sons, Ltd.     

Void growth and damage models for predicting ductile fracture in welds

This study reports on a numerical and experimental investigation of ductile tearing using a local approach to fracture. Two models have been analysed: (i) the Rice–Tracey (RT) void growth model; and (ii) the Rousselier continuum damage theory. The effects of the model parameters, including the mesh size, on the crack growth behaviour have been analysed, and a significant influence on both the J -values and the slopes d J /d a has been noted. The crack propagation in an overmatched welded joint has also been investigated. For the RT model, crack propagation has been simulated using the release node technique. Because this method requires one to previously assign the crack propagation path, using such a model is somewhat restrictive. This problem vanishes when dealing with Rousselier's model (and more generally with coupled models) because the elements which are damaged automatically give the crack path.     

Comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials

Fatigue damage prediction under a general multiaxial service loading consists of three main steps: multiaxial cycle counting, damage evaluation for an identified cycle (or reversal), and damage accumulations. The accuracy of fatigue life predictions depends on all the above steps. This paper reviews the evolutions of various multiaxial fatigue damage models, a comparative study is conducted about the physical basis, the computational efficiency, and the application range of the approaches. Based on the comparative studies, a new procedure is proposed to evaluate fatigue damage under general multiaxial random loading, which uses the Wang and Brown´s multiaxial cycle counting method for identifying cycles (or reversals), the modified procedure of the minimum circumscribed ellipse (MCE) approach for fatigue damage evaluation for an identified cycle (or reversal), and the Miner´s linear damage law for fatigue damage accumulations. By comparisons of the predicted life results with experimental results and with other approaches, it is shown that the proposed procedure is very efficient and suitable for computer aided structural optimization against fatigue.     

Numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage

This paper deals with a class of rate-independent metal plasticity models which exhibit non-linear isotropic hardening, non-linear kinematic hardening (Chaboche-Marquis model) and ductile damage (Lemaitre-Chaboche model). The backward Euler scheme is used to integrate the rate constitutive relations. The non-linear equations obtained are solved by the Newton method. The consistent tangent operator is obtained by exact linearization of the algorithm. Despite the complexity of the constitutive equations, closed-form expressions are derived, without any approximations. Analytical, numerical and experimental results are presented and discussed.     

Picosecond pump-probe absorption spectroscopy in gases: models and experimental validation

Picosecond pump-probe absorption spectroscopy is a spatially resolved technique that is capable of measuring species concentrations in an absolute sense without the need for calibrations. When laser pulses are used that are shorter than the collision time in a sample, this pump-probe technique exhibits reduced sensitivity to collisional effects such as electronic quenching. We describe modeling and experimental characterization of this technique. The model is developed from rate equations that describe the interactions of the pump and probe pulses with the sample. Calculations based on the density-matrix equations are used to identify limits of applicability for the model. Excellent agreement between the model and the experimental data is observed when both 1.3- and 65-ps pulses are used to detect potassium in a flame and in an atomic vapor cell.     

Effect of hardening models on different ductile fracture criteria in sheet metal forming

Prediction of the fracture is one of the challenging issues which gains attention in sheet metal forming as numerical analyses are being extensively used to simulate the process. To have better results in predicting the sheet metal fracture, appropriate ductile fracture criterion (DFC), yield criterion and hardening rule should be chosen. In this study, the effects of different hardening models namely isotropic, kinematic and combined hardening rules on the various uncoupled ductile fracture criteria are investigated using experimental and numerical methods. Five different ductile fracture criteria are implemented to a finite element code by the user subroutines. The criterion constants of DFCs are obtained by the related experimental tests. The in-plane principle strains obtained by the finite element analyses for different DFCs are compared with the experimental results. Also, the experimental results are used to evaluate the principle strain values calculated by the finite element analysis for different combinations of DFCs and hardening rules. It is shown that some DFCs give better predictions if the appropriate hardening model is employed.     

On continuum models of ductile fracture

Several fracture criteria are reviewed with respect to ductile fracture. It is suggested that both critical crack-tip displacement, 2V _c ^*, and critical fracture strain,∃ ^*, criteria may describe the fracture of a ductile second phase rod in a ductile matrix. As a first approximation, this is experimentally verified by observations of ductile stainless steel fibres fracturing in an age-hardened aluminium matrix. For 0.05, 0.10 and 0.20 volume fraction composites, the average fracture strains are calculated to be 1.15 as compared to a measured average of 0.93 while the average critical crack-tip displacement is calculated to be 0.50 mm as compared to an “observed” average of 0.40 mm. The statistical variation in the fracture strain was not sufficiently small to allow any choice between these proposed criteria. In fact, both the experimental and theoretical evidence point to the equivalency of these criteria as given by 2V _c ^*=π/^*∃^* where /^* is the microstructural unit in front of the crack over which the strain is greater than or equal to∃ ^*.     

Fatigue crack growth of multiple interacting cracks: Analytical models and experimental validation

This article deals with the fatigue propagation of multiple cracks in finite width holed panels, which are typical of aircraft structural components. Theoretical studies in the literature have been considered and critically analyzed. Some of them have been translated into analytical models and implemented in a computer code. To check the effectiveness of the used models, a fatigue testing campaign has been conducted on six different configurations of notches and cracks. The comparison between experimental results and those obtained from the implemented models has shown a good agreement.     

Numerical and experimental validation of computational models for mode I composite fracture failure

This work compares the numerical determination of the strain energy release rate in mode I for the interlaminar fracture of composite laminates by means of two different models: the virtual crack closure technique (VCCT) and the two-step extension method. Results were compared with empirical data obtained from double cantilever beam (DCB) tests carried out on unidirectional AS4/8552 carbon/epoxy laminates. The study showed that, in a pure mode I state, results obtained via the two-step method were in agreement with a straightforward calculation of the elastic energy variation in the system. Results from VCCT calculations were slightly lower than those obtained through the two-step method using four node elements in plane strain. As expected, results from both models converge as element length decreases.     

Numerical models of volumetric insulating cracks in eddy-current testing with experimental validation

This paper concerns fast electromagnetic modeling of volumetric cracks in conductive materials under eddy-current inspection. The underlying numerical method is described. The model is tested on cracks in aluminum structures employed in aeronautical manufacture. The computational results obtained with the method display satisfactory agreement with the respective experimental and numerical results obtained by representing cracks as nonconductive surfaces.     

A unified damage factor model for ductile fracture of steels with different void growth and shrinkage rates

Micromechanical fracture modelling is an effective method to predict ductile fracture in steel structures. This paper aims to establish a simplified and general fracture model for various loading conditions, which is convenient to calculate the instantaneous damage index. With the concept of the ductile damage factor, a unified ductile damage factor model considering the difference of rates between void growth and shrinkage has been proposed. Based on experiment results and finite element analysis, the model parameters for Q235B Chinese structural steel were calibrated. The ductile damage factor and equivalent plastic strain at fracture initiation were investigated. Comparison among the proposed model, experimental results, and the cyclic void growth model demonstrated the effectiveness and accuracy of the proposed model. A parametric study was conducted to investigate the influence of cyclic constitutive parameters on the accuracy of fracture prediction. The predicted results are acceptable while reducing those calibrated cyclic constitutive parameters by 20%.