Simulation Of Ductile Fracture Research Articles

Finite-Element Simulation of Ductile Fracture in Reduced Section Pull-Plates Using Micromechanics-Based Fracture Models

Micromechanics-based models that capture interactions of stress and strain provide accurate criteria to predict ductile fracture in finite-element simulations of structural steel components. Two such models—the void growth model and the stress modified critical strain model are applied to a series of twelve pull-plate tests that represent reduced (or net) section conditions in bolted and reduced beam section connections. Two steel varieties, A572 Grade 50 and a high-performance Grade 70 bridge steel are investigated. The models are observed to predict fracture much more accurately than basic longitudinal strain criteria, by capturing stress–strain interactions that lead to fracture. The flat stress and strain gradients in these pull plates allow the use of relatively coarse finite-element meshes providing economy of computation while capturing fundamental material behavior and offering insights into localized ductile fracture effects.

Dynamic ductile fracture in aluminum round bars: experiments and simulations

The application of rate-dependent cohesive elements is validated in simulation of ductile fracture in aluminum round bars under dynamic loading conditions. Smooth and notched round bars made of AA6060-T6 are tested and simulated under quasi-static and dynamic loadings. The smooth round bar is modeled using finite elements that obey Gurson–Tvergaard–Needleman (GTN) formulation as the constitutive equation. Comparing with experimental results, corresponding GTN parameters and rate-dependent plasticity of the alloy are obtained. A single strain rate-dependent GTN element with the obtained parameters is examined under different values of stress triaxiality and loading rates. The resulting stress-elongation curves represent the traction separation law (TSL) for cohesive elements and the variations of the maximum traction and the energy absorbed are investigated.

A robust and consistent remeshing-transfer operator for ductile fracture simulations

This paper addresses the numerical simulation of quasi-static ductile fracture. The main focus is on numerical and stability aspects related to discrete crack propagation. Crack initiation and propagation are taken into account, both driven by the evolution of a discretely coupled damage variable. Discrete ductile failure is embedded in a geometrically nonlinear hyperelasto-plastic model, triggered by an appropriate criterion that has been evaluated for tensile and shear failure. A crack direction criterion is proposed, which is validated for both failure cases and which is capable of capturing the experimentally observed abrupt tensile–shear transition. In a large strain finite element context, remeshing enables to trace the crack geometry as well as to preserve an adequate element shape. Stability of the computations is an important issue during crack propagation that can be compromised by two factors, i.e. large stress redistributions during the crack opening and the transfer of variables between meshes. A numerical procedure is developed that renders crack propagation considerably more robust, independently of the mesh fineness and crack discretisation. A consistent transfer algorithm and a crack relaxation method are proposed and implemented for this purpose. Finally, illustrative simulations are compared with published experimental results to highlight the features mentioned.

An integrated continuous–discontinuous approach towards damage engineering in sheet metal forming processes

This paper addresses the simulation of ductile damage and fracture in metal forming processes. A combined continuous–discontinuous approach has been used, which accounts for the interaction between macroscopic cracks and the surrounding softening material. Softening originates from the degradation processes taking place at a microscopic level, and is modelled using continuum damage mechanics concepts. To avoid pathological localisation and mesh dependence and to incorporate length scale effects due to microstructure evolution, the damage growth is driven by a non-local variable via a second order partial differential equation. The two governing equations, i.e. equilibrium and non-local averaging, are solved in an operator-split manner. This allows one to use a commercial finite element software to solve the equilibrium problem, including contact between the tools and work piece. The non-local averaging equation is solved on a fixed configuration, through a special purpose code which interacts with the commercial code. A remeshing strategy has been devised that allows: (i) to capture the localisation zone, (ii) prevent large element distortions and (iii) accommodate the crack propagation. To illustrate the capabilities of the modelling tool obtained by combining these continuum mechanics concepts and computational techniques, process simulations of blanking, fine-blanking and score forming are presented.

Meshfree simulations of thermo-mechanical ductile fracture

In this work, a meshfree method is used to simulate thermo-mechanical ductile fracture under finite deformation. A Galerkin meshfree formulation incorporating the Johnson-Cook damage model is implemented in numerical computations. We are interested in the simulation of thermo-mechanical effects on ductile fracture under large scale yielding. A rate form adiabatic split is proposed in the constitutive update. Meshfree techniques, such as the visibility criterion, are used to modify the particle connectivity based on evolving crack surface morphology. The numerical results have shown that the proposed meshfree algorithm works well, the meshfree crack adaptivity and re-interpolation procedure is versatile in numerical simulations, and it enables us to predict thermo-mechanical effects on ductile fracture.

Simulation of Ductile Fracture of Circular Hollow Section Joints Using the Gurson Model

Numerical modeling of the fracture effects on the strength of steel circular hollow section joints has not been sufficiently addressed historically. The Gurson model simulates the plastic yield behavior of material with microvoids. It is found in the current study that we can offer an alternative approach in modeling the ductile fracture for the strength analysis of tubular joints. Two loading conditions are investigated on tubular bars with the Gurson model. The effects of void growth and nucleation are observed to be more prominent in the axial tensile mode than the shear mode. Two types of tubular joints are investigated: precracked tubular joints and intact tubular joints. The effect of ductile fracture is reflected by softening of material, which leads to reductions in load-deformation curves which are consistent with test observations. Due to the lack of material data, a sensitivity study is carried out on the Gurson's material properties.

Theoretical and Experimental Damage Prediction in Cold and Semi‐Hot Bulk Forming of Ductile Steels

Bulk forging is among the most important manufacturing methods in metal forming, due to its wide applicability from some ounces to several tons of steel in a high diversity of shapes and forming conditions. Economical constraints demand for further optimisation and cost‐effective production. This requires the application of suitable finite elements simulation software, in order to support the already digitalised construction processes. Ductile damage is one of the most severe problems to arise during the production sequences, not only in cold but also in semi‐hot forging operations. Mathematical approaches exist for the modelling and simulation of ductile fracture in steel. In this paper some widespread used damage models are introduced and discussed. Their damage prediction quality has been verified by experiments, the tensile test and the collar specimen upsetting with several different steels under cold and semi‐hot forging conditions. The methods for the experimental fracture detection are introduced as well. In cold forging the passive ultrasonic testing with integrated statistical filtering algorithms is used. As this method is not applicable to semi‐hot forging experiments, optical fracture detection by means of a high‐speed camera is used instead. A very interesting material behaviour of the steels tested has been identified in the semi‐hot upsetting of collar specimen. For every steel a distinct temperature crossover interval exists, in which the forging process abruptly changes from damaged to undamaged state. This interval amounts to some degrees Celsius only for each of the seven materials investigated. Among the damage models proposed, the Model of Effective Stresses by Lemaitre is chosen for the application to a cold and a semi‐hot forging operation. These industrial processes of an axle end (cold) and a journal bearing (semi‐hot) are susceptible to damage for reasons to be discussed in this paper. It will be shown that the internal fracture of the axle end (chevrons) and the surface fissures of the journal bearing can be predicted with high accuracy. Moreover, the application of the damage model in the finite element software MSC.SuperForm 2004 offers a promising approach for process optimisation. Several possibilities could be tested for their suitability of reducing the calculated damage: geometry variation of the forming tools, process annealing, different materials. The use of damage models in finite element simulation can be regarded as a further step towards an optimal process design.

Ductile Fracture Simulation of Structural Steel Components Using the Local Approach

Ductile Fracture Simulation of Structural Steel Components Using the Local Approach

A numerical approach for the simulation of ductile fracture with embedded discontinuities

AbstractIn the present study, a computational approach for the numerical simulation of ductile fracture within the framework of the finite element method is proposed. In the developed macroscopic formulation, the inelastic behavior in the bulk of the material is described by the finite elasto‐plastic material model proposed in [4]. The failure process is modeled by introducing discontinuities when a special local fracture criterion is satisfied. The discontinuities are incorporated via special triangular finite elements with embedded interfaces following the line of [2]. Finally, the numerical procedure is evaluated for a twodimensional representative test problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mesh‐free simulation of ductile fracture

AbstractThis paper is concerned with mesh‐free simulations of crack growth in ductile materials, which is a major technical difficulty in computational mechanics. The so‐called reproducing kernel particle method, which is a member of the mesh‐free method family, is used together with the Gurson–Tvergaard–Needleman constitutive model for simulation of ductile fracture. A study has been carried out to compare the proposed mesh‐free simulation with the available experimental results and previous finite element simulations for crack propagation in a three‐point‐bending steel specimen. The results show that the mesh‐free simulation agrees well with experimental results, and it is confirmed that the proposed method provides a convenient and yet accurate means for simulation of ductile fracture. Copyright © 2004 John Wiley & Sons, Ltd.

Simulation of brittle and ductile fracture in an impact loaded prenotched plate

We analyze the initiation and propagation of a crack from a point on the surface of a circular notch-tip in an impact loaded prenotched plate. The material of the plate is assumed to exhibit strain hardening, strain-rate hardening, and softening due to the rise in temperature and porosity. The degradation of material parameters due to the evolution of damage in the form of porosity is considered. Brittle failure is assumed to initiate when the maximum tensile principal stress at a point reaches a critical level. Ductile failure is assumed to ensue when the effective plastic strain reaches a critical value. A crack initiating from the node where a failure first occurs is taken to propagate to the adjacent node that has the highest value of the failure parameter (the maximum tensile principal stress or the effective plastic strain). The opening and propagation of a crack are modeled by the node release technique. Surface tractions and the normal component of the heat flux are taken to be null on the newly created crack surfaces. For the brittle failure, the stress field around the crack tip resembles that in mode-I deformations of a prenotched plate loaded in tension. The distribution of the effective plastic strain in a small region around the surface of the notch-tip is not affected much by the initiation of a ductile fracture there except for a shift in the location of the point where the effective plastic strain is maximum. The initiation of the ductile failure is delayed when a crack is opened at the point where the brittle failure ensues.

Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels

A multi-scale hierarchical constitutive model is developed for establishing the relationship between quantum mechanical, micromechanical, and overall strength/toughness properties in steel design. Focused on the design of ultra-high strength, high toughness steels, a two-level cell model is used to represent two groups of hard particles (inclusions) in an alloy matrix which is characteristic of such Fe-based alloys. Primary inclusion particles, which are greater than a micron in size, are handled by a microcell. Secondary inclusion particles which are tens of nanometers in size are modeled by a sub-microcell. In the sub-microcell, the matrix constitutive behavior is given by quantum mechanics computation of bcc-iron calibrated according to experiments. In the microcell, the matrix constitutive behavior is given by the stress–strain response of the sub-microcell, characterized by a plastic flow potential based on the numerical simulation of the representative cell. In turn, the plastic flow potential generated by the stress–strain response of the microcell is used as the constitutive response at the continuum macro level for simulation of ductile fracture and for the assessments of toughness. The interfacial debonding between the matrix and the primary and the secondary inclusion particles are modeled using decohesion potentials computed through quantum mechanics calculation together with a mechanical model of normal separation and gliding induced dislocation, which also provides quantitative explanations why practice strength of a steel is much lower than the atomic separation force and how plasticity occurs in steels. The ductile fracture simulations on an ASTM standard center cracked specimen lead to the generation, for the first time, of a toughness, strength, adhesion diagram based on computer simulation and which establishes the relationship between alloy matrix strength, interfacial decohesion energy, and fracture toughness.

Numerical Simulation of Ductile Fracture Based on Local Approach Concept

In this paper a finite-element analysis on ductile fracture in two-dimensional quasi-static state is performed by using the local approach concept in continuum damage mechanics. An isotropic damage model based on the generalized concept of effective stress is proposed. Crack propagation is achieved by removing critically damaged elements. The finite-element approximation of a largely deforming body based on the incremental total Lagrangian concept is carried out. As numerical examples, the mesh size sensitivity analysis and the simulation of the shearing mode failure in plane strain state are carried out to verify the present formulation qualitatively. For an edge cracked plate under plane stress state, load-displacement curves and successively fractured shapes are shown. It can be concluded that the proposed model may be stated as a reasonable tool to explain ductile fracture initiation and crack propagation.

Numerical simulation of ductile fracture during high strain rate deformation

A numerical integration scheme is presented for integration of the pressure-sensitive yield criterion due to Gurson, suitable for explicit dynamic finite element calculations. This scheme utilizes a sub-increment approach to Mayntain stability for the large strain increments and intense triaxiality that can occur under high strain rate loading. A number of validation problems are presented after which two laboratory-scale high strain experiments are simulated. The integration scheme is shown to be stable and to capture the onset of tensile fracture under high strain rate loading conditions.

Finite element modelling of crack propagation in ductile fracture

In this communication, a new approach is introduced for handling finite elements in the automatic simulation of ductile fracture. The method allows for the automatic elimination of elements based on criteria such as critical plastic strain or stress triaxiality. Details of the implementation of this crack propagation method into a commercial finite element code are described. The method is applied to shear band failure and cavity nucleation

A computational procedure for the simulation of ductile fracture with large plastic deformation

It is now well-known that the applicability of the single-parameter J-approach is restricted only to high constraint crack geometries and materials of low ductility. Consequently, there is a need to develop a ductile fracture criterion that does not suffer from the geometry dependence exhibited by the J-integral. However, the ability of any analytical model to provide accurate description of fracture initiation and propagation in a ductile material is contingent upon its capability to model the large deformations that occur in the fracture process zone. The purpose of this paper is to describe the formulation and implementation of an efficient finite deformation algorithm that can be used for the prediction of elasto-plastic fracture in ductile materials where J-dominance is violated. An incrementally objective mid-interval integration algorithm is used in conjunction with an efficient polar decomposition scheme for the accurate integration of the plasticity equations in the presence of large deformations. Both rate-dependent and rate-independent plasticity models are included. A sophisticated node release algorithm for the simulation of crack propagation is also implemented. The application of continuum damage models as potential ductile fracture criteria is discussed. The overall efficiency of the code is enhanced by means of the BFGS (Broyden, Fletcher, Goldfarb and Shanno) solution algorithm. Three elasto-plasticity problems that involve finite deformation are analyzed in order to assess the accuracy of the solution procedure. The effectiveness of including material damage in the constitutive behavior to predict ductile failure in a notched tensile specimen is addressed

Computer simulation of ductile fracture in a random distribution of voids

A theory is developed to calculate the fracture strain in a material with a random distribution of voids. The voids are of equal size and are cylindrical in shape with a square cross section. Random arrays of voids are generated using a computer. The material is assumed to be rigid and perfectly plastic and is exposed to plane strain tension. The theory is based on the assumption that the material deforms homogeneously until localized deformation along a row of voids intervenes. Upper-bound solutions are used to derive criteria for the onset of inhomogeneous deformation. The fracture is assumed to occur so rapidly after the beginning of localized deformation that the fracture strain is equal to the strain to inhomogeneous deformation. Several fracture paths have been selected from the computer-generated arrays of voids and the fracture strain has been computed as a function of the tensile hydrostatic pressure. the fracture propagates along the path in the material which has the smallest fracture strain. Distribution functions are presented for intervoid spacings along the fracture paths. The study includes two volume fractions of voids: 4% and 0.25%.