A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: material model and strain localization analysis

Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.Peer ReviewedPostprint (author's final draft

Crashworthiness assessment considering the dynamic damage and failure of a dual phase automotive steel

Analyzing crash worthiness of the automotive parts has been posing a great challenge in the sheet metal and automotive industry since several decades. The present contribution will focus on one of the most urging challenges of the crash worthiness simulations, namely, an enhanced constitutive formulation to predict the failure and cracking of structural parts made from high strength steel sheets under impact. A hybrid extended Modified Bai Wierzbicki damage plasticity model is devised to this end. The material model calibrated using the experimental data covering high strain rate deformation, damage and failure successfully predicted the instability and subsequent response of the crash box under impact. Simulation results provide the deformation shape and deformation energy in order to predict and evaluate the vehicle crashworthiness. The simulations further helped in discovering the irrefutable impact of strain rate and stress state on the impact response of the auto-body structure. The strain rate is found to adequately affect the energy absorption capacity of the crash box structure both in terms of impact load and fold formation whereas the complex stress state has a direct association to the development of instability within the structure and early damage appearance within the folds

3D discrete element modeling of concrete: study of the rolling resistance effects on the macroscopic constitutive behavior

The Discrete Element Method (DEM) is appropriate for modeling granular materials [14] but also cohesive materials as concrete when submitted to a severe loading such an impact leading to fractures or fragmentation in the continuum [1, 5, 6, 8]. Contrarily to granular materials, the macroscopic constitutive behavior of a cohesive material is not directly linked to contact interactions between the rigid Discrete Elements (DE) and interaction laws are then defined between DE surrounding each DE. Spherical DE are used because the contact detection is easy to implement and the computation time is reduced in comparison with the use of 3D DE with a more complex shape. The element size is variable and the assembly is disordered to prevent preferential cleavage planes. The purpose of this paper is to highlight the influence of DE rotations on the macroscopic non-linear quasi-static behavior of concrete. Classically, the interactions between DE are modeled by spring-like interactions based on displacements and rotation velocities of DE are only controlled by tangential forces perpendicular to the line linking the two sphere centroids. The disadvantage of this modeling with only spring-like interactions based on displacements is that excessive rolling occurs under shear, therefore the macroscopic behavior of concrete is too brittle. To overcome this problem a non linear Moment Transfer Law (MTL) is introduced to add a rolling resistance to elements. This solution has no influence on the calculation cost and allows a more accurate macroscopic representation of concrete behavior. The identification process of material parameters is given and simulations of tests performed on concrete samples are shown

2nd International Workshop on Physics-Based Modelling of Material Properties and Experimental Observations with special focus on Fracture and Damage Mechanics: Book of Abstracts

This report covers the book of abstracts of the 2nd International Workshop on Physics Based Modelling of Material Properties and Experimental Observations, with special focus on Fracture and Damage Mechanics. The workshop is organized in the context of European Commission’s Enlargement and Integration Action, by the Joint Research Centre in collaboration with the TOBB University of Economics and Technology (TOBB ETU) on 15th-17th May 2013 in Antalya, Turkey. The abstracts of the keynote lectures and all the technical presentations are included in the book. This workshop will give an overview of different physics-based models for fracture and degradation of metallic materials and how they can be used for improved understanding and more reliable predictions. Models of interest include cohesive zones to simulate fracture processes, ductile-brittle transition for ferritic steels, ductile fracture mechanisms such as void growth or localized shear, fatigue crack initiation and short crack growth, environmental assisted cracking. Experimental studies that support such models and case studies that illustrate their use are also within the scope. The workshop is also an opportunity for scientists and engineers from EU Member States and target countries to discuss research activities that could be a basis for future collaborations.JRC.F.4-Nuclear Reactor Integrity Assessment and Knowledge Managemen

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

Crackling noise in three-point bending of heterogeneous materials

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting time distributions have a power law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasi-brittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.Comment: 11 pages, 15 figure

Simulation of dynamic fracture in aluminum structures

The present thesis treats the simulation of crack initiation and growth by the use of cohesive zone models under dynamic loading conditions . The first chapter reviews the aspects of fracture mechanics that are related to the subject. The rest of the thesis consists of two self-contained articles and one conference paper. Finite element models containing rate dependent cohesive elements have been introduced in the papers. The rate dependency of cohesive elements is obtained through calculations on single elements obeying rate dependent Gurson type equations. The papers represent three main aspects: model establishment, validation, and application. In the first article, the aim is to establish a model which has the ability to account for crack growth simulations under dynamic loading conditions. A rate-dependent Gurson type model has been used to define rate and triaxiality dependency of cohesive elements. The rate- and triaxiality-dependent cohesive elements are used in a finite element model to simulate crack propagation in a middle-cracked tension M(T) specimen made of aluminum alloy. The calculations show the importance of strain rate and stress triaxiality on the rate of the crack growth and the change of the load. The second paper examines the validation of the rate sensitive cohesive elements and the proposed procedure by comparing the results of the simulations and experiments on aluminum round bars under dynamic loading conditions. Smooth and notched round bars are tested and simulated and the load-diameter reduction curves are compared. The third paper applies the model to a bi-material (laser welded) compact tension C(T) specimen under dynamic loading conditions. The specimen made of aluminum alloy contains an initial crack on the interface of fusion zone and base metal. The crack growth is simulated by rate dependent cohesive elements which are oriented in different directions so that mixed mode crack propagation is feasible. The articles show the importance of considering rate dependency in the calculation of both the energy dissipated by plastic deformation and the energy of separation. They also show that the approach used is convenient for the simulation of dynamic ductile crack initiation and growth. The procedure considered can also be used for other areas of fracture simulation where the energy of separation is a function of variables that exist at the crack tip area.PhD i produktutvikling og materialerPhD in Engineering Design and Material

ON MULTISCALE DAMAGE MODELLING OF HETEROGENEOUS MATERIALS USING NONLOCAL CONTINUUM THEORY

An overview of the modelling of quasi-brittle as well as ductile damage is given. The multiscale procedure employing the nonlocal continuum theory is described in more detail. The softening is introduced at the microlevel in the microstructural volume element and after that the homogenization procedure state variables are mapped at the macrolevel material point via the scale transition approach. In the case of quasi-brittle softening the C1 continuous finite element discretization is applied at both micro- and macrolevel. At the modelling of ductile damage response, the macrolevel is also discretized by the C1 finite element formulation, while the microscale utilizes quadrilateral mixed finite elements employing the nonlocal equivalent plastic strain and gradient-enhanced elastoplasticity. All approaches presented are verified in the standard examples