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Register a new userNonlocal Damage-enhanced Plasticity Model for Ductile Fracture Analysis Using a Lattice Particle Method
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Ductile fracture of metallic materials typically involves the elastoplastic deformation and associated damaging process. A nonlocal lattice particle method (LPM) is proposed to model this complex behavior. Recently, a distortional energy-based model is formulated into LPM to simulate the mixed linear hardening J2 plasticity. However, this model is based on the incremental updating algorithm which needs very small loading steps to get reasonable results. This is time-consuming and unstable for large systems. Therefore, in this paper, a stress-based return-mapping algorithm for simulating J2 plasticity is proposed to deal with these deficiencies. The material deterioration process is reformulated as a nonlocal damage evolution process. By incorporating the iterative solution procedure with dense-packing lattices, the damage-enhanced LPM framework is able to effectively reduce the lattice-dependency of crack grow analysis. The particle-size dependency of macroscopic mechanical responses is also handled properly by using the proposed nonlocal damage model. Several numerical examples are provided to show the ability of the new LPM framework to predict the elastoplastic behavior of engineering structures with/without damage and fracture.
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Size effects have been predicted at the micro- or nano-scale for porous ductile materials from Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Mechanics numerical simulations, as a consequence of Geometrically Necessary Dislocations or due to the presence of a void matrix interface. As voids size decreases, higher stresses are needed to deform the material, for a given porosity. However, the majority of the homogenized models for porous materials used in ductile fracture modeling are size-independent, even though micrometric or nanometric voids are commonly observed in structural materials. Based on yield criteria proposed in the literature for nanoporous materials, a size-dependent homogenized model for porous materials is proposed for axisymmetric loading conditions, including void growth and coalescence as well as void shape effects. Numerical implementation of the constitutive equations is detailed. The homogenized model is validated through comparisons to porous unit cells finite element simulations that consider interfacial stresses, consistently with the model used for the derivation of the yield criteria, aiming at modeling an additional hardening at the void matrix interface. Potential improvements of the model are finally discussed with respect to the theoretical derivation of refined yield criteria and evolution laws.
A new gradient-based formulation for predicting fracture in elastic-plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material deformation is characterised by a mechanism-based strain gradient constitutive model. This non-local plastic-damage formulation is numerically implemented and used to simulate fracture in several paradigmatic boundary value problems. The case studies aim at shedding light into the role of the plastic and fracture length scales. It is found that the role of plastic strain gradients is two-fold. When dealing with sharp defects like cracks, plastic strain gradients elevate local stresses and facilitate fracture. However, in the presence of non-sharp defects failure is driven by the localisation of plastic flow, which is delayed due to the additional work hardening introduced by plastic strain gradients.
Notched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the structural strength and crack-growth-path of U-notched specimens made of brittle materials. For this purpose, the Fragile Points Method (FPM), as previously proposed by the authors, has been augmented by an interface damage model at the interfaces of the FPM domains, to simulate crack initiation and development. The formulations of FPM are based on a discontinuous Galerkin weak form where point-based piece-wise-continuous polynomial test and trial functions are used instead of element-based basis functions. In this work, the numerical fluxes introduced across interior interfaces between subdomains are postulated as the tractions acting on the interface derived from an interface damage model. The interface damage is triggered when the numerical flux reaches the interface strength, and the process of crack-surface separation is governed by the fracture energy. In this way, arbitrary crack initiation and propagation can be naturally simulated without the need for knowing the fracture-patch before-hand. Additionally, a small penalty parameter is sufficient to enforce the weak-form continuity condition before damage initiation, without causing problems such as artificial compliance and numerical ill-conditioning. As validations, the proposed FPM method with the interface damage model is used to predict the structural strength and crack-development from U-notched structures made of brittle materials, which is useful but challenging in engineering structural design practices.
We present a stochastic modeling framework for atomistic propagation of a Mode I surface crack, with atoms interacting according to the Lennard-Jones interatomic potential at zero temperature. Specifically, we invoke the Cauchy-Born rule and the maximum entropy principle to infer probability distributions for the parameters of the interatomic potential. We then study how uncertainties in the parameters propagate to the quantities of interest relevant to crack propagation, namely, the critical stress intensity factor and the lattice trapping range. For our numerical investigation, we rely on an automated version of the so-called numerical-continuation enhanced flexible boundary (NCFlex) algorithm.
Ebert et al. [Phys. Rev. Lett. 77, 3827 (1996)] have fractured icosahedral Al-Mn-Pd single crystals in ultrahigh vacuum and have investigated the cleavage planes in-situ by scanning tunneling microscopy (STM). Globular patterns in the STM-images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high symmetry axes. From detailed analyses of the fractured samples we conclude that both, the plane structure and the clusters, strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.
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