Non-local regularization for FE simulation of damage in ductile materials

The paper presents an application of the non-local regularization to the finite element modelling of ductile damage and tearing. In order to model the damage growth in ductile materials of structural components, integral limiters have been introduced. These integral limiters, which are spatial averaging operators, can prevent the problem of mesh-sensitivity of the finite element computations. Hence, it was important to establish the characteristic length l_c for spatial averaging operators of the non-local regularization. More formally, the in-plane distance l_c and the out-of-plane FE dimension have been specified, characterizing the volume over which averaging of stress and strain was carried out to ensure that the continuum theory can represent the physical process of damage.

In order to check the reliability and transferability of the method, FE simulations of various testing examples have been carried out, namely ductile fracture in notched tensile specimens, ductile crack growth in C(T) specimens and application to the pipe-bending test.     

A probabilistic fracture mechanics model including 3D ductile tearing of bi-axially loaded pipes with surface cracks

This paper presents a probabilistic fracture mechanics model established from three-dimensional FEM analyses of surface cracked pipes subjected to tension load in combination with internal pressure. The models are particularly interesting for offshore pipelines under operational conditions or during laying, where inelastic deformations may occur. In the numerical models, the plastic deformations, including ductile tearing effects, are accounted for by use of the Gurson-Tvergaard-Needleman model. This model is calibrated to represent a typical X65 pipeline steel behaviour under ductile crack growth and collapse. Several parameters are taken into account, such as crack depth, crack length and material hardening. Another important topic is the examination of the influence of bi-axial loading due to internal pressure on capacity. From the results of the deterministic analyses a probabilistic fracture mechanics model is established using the response surface methodology. Two failure criteria are examined to represent the structural capacity. Based on the established model, we illustrate the methodology by examples employing the two different failure criteria solved with first and second order reliability methods.     

Calibration procedures for a computational model of ductile fracture

A recent extension of the Gurson constitutive model of damage and failure of ductile structural alloys accounts for localization and crack formation under shearing as well as tension. When properly calibrated against a basic set of experiments, this model has the potential to predict the emergence and propagation of cracks over a wide range of stress states. This paper addresses procedures for calibrating the damage parameters of the extended constitutive model. The procedures are demonstrated for DH36 steel using data from three tests: (i) tension of a round bar, (ii) mode I cracking in a compact tension specimen, and (iii) shear localization and mode II cracking in a shear-off specimen. The computational model is then used to study the emergence of the cup-cone fracture mode in the neck of a round tensile bar. Ductility of a notched round bar provides additional validation.     

Identification of ductile damage and fracture parameters from the small punch test using neural networks

This paper presents a method for the identification of deformation, damage and fracture properties of ductile materials. The small punch test is used to obtain the material response under loading. The resulting load displacement curve contains information about the deformation and failure behavior of the tested material. The finite element method is used to compute the load displacement curve depending on the parameters of the Gurson-Tvergaard-Needleman damage law. Via a systematic variation of the material parameters a data base is built up, which is used to train neural networks. This neural network can be used to predict the load displacement curve of the SPT for a given material parameter set. The identification of the material parameters is done by using a conjugate directions algorithm, which minimizes the error between an experimental load displacement curve and one predicted by the network function. The identified material parameters are validated by independent tests on notched tensile specimens. Furthermore, these parameters can be used to compute the crack growth in fracture specimens, which finally leads to a prediction of classical fracture toughness parameters.     

Essential work of fracture analysis of the tearing of a ductile polymer film

The fracture behaviour of a 0.5 mm thick ethylene-propylene block copolymer, previously evaluated using the essential work of fracture method, has been analyzed again in more detail, using different plots, allowing the determination of the crack initiation displacement and stress. In such plots is evidenced that the specific essential work of fracture, w_e, corresponds to the energy just up to crack initiation value that can be related with J₀. Also, it has been found a novel relationship between the plastic term, βw_p and the crack initiation stress, σ_i.     

h-Hierarchical functions for 2D and 3D BEM

In this paper, it is shown that the idea of hierarchical BEM formulations can be extended in a systematic way to the h-method, and that the accuracy obtained with h-hierarchical shape functions is the same as for standard shape functions of the same order (i.e. the two functional spaces are identical). A rigorous way of obtaining new h-hierarchical shape functions in BEM is developed and put into effect for both two-dimensional quadratic and three-dimensional quadrilateral quadratic elements.     

A direct method for calculating the stress intensity factor in BEM

The proposed algorithm employs singular crack tip elements in which the stress intensity factor appears as a degree of freedom. The additional degrees of freedom are compensated by constraint conditions which originate from imposing continuity across elements and a contour integration formula. The two benchmark problems indicate the proposed algorithm can accurately predict the stress intensity factor and the distribution of the primary and secondary variables in fracture problems.     

Numerical simulations of void linkage in model materials using a nonlocal ductile damage approximation

Experiments on the growth and linkage of 10 μm diameter holes laser drilled in high precision patterns into Al-plates were modelled with finite elements. The simulations used geometries identical to those of the experiments and incorporated ductile damage by element removal under the control of a ductile damage indicator based on the micromechanical studies of Rice and Tracey. A regularization of the problem was achieved through an integral-type nonlocal model based on the smoothing of the rate of a damage indicator D over a characteristic length L. The simulation does not predict the experimentally observed damage acceleration either in the case where no damage is included or when only a local damage model is used. However, the full three-dimensional simulations based on the nonlocal damage methodology do predict both the failure path and the failure strain at void linkage for almost all configurations studied. For the cases considered the critical parameter controlling the local deformations at void linkage was found to be the ratio between hole diameter and hole spacing.     

Incremental damage theory of particulate-reinforced composites with a ductile interphase

This paper deals with a new micromechanics model of particulate-reinforced composites (PRCs) describing the evolution of debonding damage, matrix plasticity and particle size effect on the deformation. A ductile interphase was considered in the frame of incremental damage theory to analyze the dependence of elastic–plastic–damage behavior on particle size. Progressive debonding damage was controlled by a critical energy criterion for particle–matrix interfacial separation. The equivalent stresses of the matrix and interphase were determined by field fluctuation method. The influences of progressive debonding damage, particle size and interphase properties on the overall stress–strain response of PRC were explained simultaneously. Due to the existence of a ductile interphase, stress transfer and plastic initiation in PRC become very complicated, and thus a unit-cell (UC) based FEM was used to simulate their evolutions and demonstrate the role of the interphase. Finally, particle size effect on the mechanical behaviors of composites was interpreted.     

3D fracture analysis by the symmetric Galerkin BEM

 The subject of this paper is the formulation and the implementation of the symmetric Galerkin BEM for three-dimensional linear elastic fracture mechanics problems. A regularized version of the displacement and traction equations in weak form is adopted and the integration techniques utilized for the evaluation of the double surface integrals appearing in the discretized equations are detailed. By using quadratic isoparametric quadrilateral and triangular elements, some example crack problems are solved to assess the efficiency and robustness of the method. Received 6 November 2000     

The radial integration method for evaluation of domain integrals with boundary-only discretization

In this paper, a simple and robust method, called the radial integration method, is presented for transforming domain integrals into equivalent boundary integrals. Any two- or three-dimensional domain integral can be evaluated in a unified way without the need to discretize the domain into internal cells. Domain integrals consisting of known functions can be directly and accurately transformed to the boundary, while for domain integrals including unknown variables, the transformation is accomplished by approximating these variables using radial basis functions. In the proposed method, weak singularities involved in the domain integrals are also explicitly transformed to the boundary integrals, so no singularities exist at internal points. Some analytical and numerical examples are presented to verify the validity of this method.     

Regularized algorithms for the calculation of values on and near boundaries in 2D elastic BEM

It is verified that, under certain continuity conditions, the boundary integral equations (BIEs) of both displacement and displacement derivative can be expressed in a variety of regularized forms with at most weak singularities for any points within the domain or on its boundary. A series of algorithms embedded in the regularized formulations are presented to calculate the field variables within the domain or on its boundary. Detailed numerical results are given to check and compare the validities of the proposed algorithms and some practical effective algorithms are discovered. Due to the character of the at most weak singularities in the formulations, the algorithms require no special numerical treatments, but only the general Gauss quadrature to implement. To the end, the continuity requirements for the field variables and the validities of the algorithms are discussed.     

Spallation caused by the diffusion and agglomeration of vacancies in ductile metals

In this paper, the spallation process for the ductile metals under plane shock loading is discussed in theory. By employing the phase transition theory and non-equilibrium theory, the spallation process may be understood as a result of the diffusion and agglomeration of the generated vacancies. Through the detailed theoretical analysis, the following important points are concluded: (1) the spalling temperature, a new concept, is proposed first and the appearance of spallation critical behavior is proved; (2) the quantitative grain size, tensile strain rate and temperature dependence of both the damage evolution rate and the void growth velocity is obtained; (3) the existence of a characteristic size for the voids and a characteristic stress at the void boundary is discovered first, and their magnitude depend on the vacancy excitation energy and the average volume of one vacancy; (4) the temperature of metal near the growing void is found to be high, possibly causing the metal to melt, and it decreases quickly with the distance away from the void; (5) the area of the plastic zone, surrounding one formed spherical void, is clarified; (6) the viewpoint is put forward that the void growth may arise from the agglomeration of vacancies rather than the emission of dislocations when the shocking temperature approaches spalling temperature. Most of the above theoretical results are novel and obtained first.     

BEM and FEM analysis of Signorini contact problems with friction

In this paper, we present a comparative study of the boundary element method (BEM) and the finite element method (FEM) for analysis of Signorini contact problems in elastostatics with Coulomb's friction law. Particularities of each method and comparison with the penalty method are discussed. Numerical examples are included to demonstrate the present formulations and to highlight its performance.     

Defect tolerance assessment of ARIANE 5 structures on the basis of damage mechanics material modelling

Damage mechanics based material models have been applied to establish fracture control procedures for the failure prediction of ARIANE 5 main structural components as the booster cases including welds, the main stage, and the upper stage cryogenic tank. The main goals of the damage mechanics based investigations were the accurate failure prediction, the clarification of dependency of fracture toughness on geometry, the calibration of analytical methods and the interpretation and optimisation of small scale fracture tests for material characterization and quality assurance.The results of these investigations allowed a failure prediction accuracy with analytical tools which is close to 3D numerical simulations. This could be demonstrated both with ductile (Gurson) and brittle (RKR) damage mechanics models.     

Experimental and numerical investigation on ductile fracture mechanism of aluminium alloy using new modified model

In the present paper, the ductile fracture of aluminium alloy 5052P-H34 is studied by experiments and simulations. Then, the extension of the damage growth model, which captures both tension as well as shear, was employed in the present paper, and a modified Rousselier model was proposed. A stress integration algorithm based on the general backward Euler return algorithm was developed and implemented into finite element (FE) models in the ABAQUS/Explicit platform. The shear coefficient was calibrated by a FE analysis based on an inverse calibration procedure combined with the physical experiments. The predictive capability of this model was studied by comparing the experiments with the simulations, and the validity of this model was verified. The results show that the modified Rousselier model can give more accurate results for both tension and shear failure.     

Revisit of degenerate scales in the BIEM/BEM for 2D elasticity problems

The boundary integral equation method in conjunction with the degenerate kernel, the direct searching technique (singular value decomposition), and the only two-trials technique (2 × 2 matrix eigenvalue problem) are analytically and numerically used to find the degenerate scales, respectively. In the continuous system of boundary integral equation, the degenerate kernel for the 2D Kelvin solution in the polar coordinates is reviewed and the degenerate kernel in the elliptical coordinates is derived. Using the degenerate kernel, an analytical solution of the degenerate scales for the elasticity problem of circular and elliptical cases is obtained and compared with the numerical result. Further, the triangular case and square case were also numerically demonstrated.     

Numerical study on the effect of prestrain history on ductile fracture resistance by using the complete Gurson model

During installation and operation, pipeline steels may suffer from plastic pre-deformation (prestrain) due to accidental loading, cold bending or ground movement. The plastic prestrain history not only modifies steels’ yield and flow properties but also influences their fracture performance. This paper focuses on the effect of plastic prestrain history on ductile fracture resistance. Single edge notched tension (SENT) specimens have been selected for the numerical study and the crack is assumed to exist before a prestrain history was applied. The complete Gurson model has been applied to simulate the ductile fracture behaviour. The results show that prestrain history can reduce the fracture resistance significantly and neither the history-independent resistance model nor material-memory resistance model existing in the literature can be used to describe the prestrain history effect. Based on the numerical results an approximate history-dependent resistance model is proposed. The results also suggest that it is important to take the prestrain effect into consideration in future structural integrity assessment procedure for pipelines.     

Micromechanical modelling of ductile crack growth in the binder phase of WC–Co

This study focuses on numerical simulation of ductile failure in the Co binder phase of WC–Co hardmetal. The growth of edge cracks under mode I loading is considered. A computational micromechanics approach is taken where the Co binder ligaments are explicitly represented in finite element models. An embedding technique is employed. Crystal plasticity theory is used to represent plastic deformation in the Co ligaments. Crack propagation in the binder is simulated using an element removal technique based on a modified Rice and Tracey model for ductile void growth, and fracture resistance curves are generated. Parameter studies are performed for variations in microstructrual parameters such as numbers of Co ligaments ahead of the crack tip and local Co volume fraction. The importance of thermal residual stresses and finite element mesh density are also investigated.