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Journal ArticleDOI

Numerical modelling of ductile spall fracture

01 Apr 1995-International Journal of Impact Engineering (Pergamon)-Vol. 16, Iss: 2, pp 237-251
TL;DR: In this paper, a macroscopic constitutive equation for porous materials, which is based on a void growth model under the combined action of hydrostatic and deviatoric stresses, is presented.
About: This article is published in International Journal of Impact Engineering.The article was published on 1995-04-01. It has received 5 citations till now. The article focuses on the topics: Spall & Porosity.
Citations
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Journal ArticleDOI
TL;DR: In this article, a Critical Damage Evolution (CDE) model considering void growth and coalescence is proposed for describing the dynamic tensile spall of ductile metals sustaining intense dynamic loading.

22 citations

Dissertation
29 Apr 2013
TL;DR: In this paper, a critical review of the constitutive modeling of materials subjected to large strains and high to very high strain rate behavior of materials and components is presented, and the results are compared to those obtained from the original Johnson-Cook model.
Abstract: The present doctoral thesis deals with the study and the analysis of large strain and high strain rate behavior of materials and components. Theoretical, experimental and computational aspects are taken into consideration. Particular reference is made to the modeling of metallic materials, although other kinds of materials are considered as well. The work may be divided into three main parts. The first part of the work consists in a critical review of the constitutive modeling of materials subjected to large strains and high to very high strain rates. Specific attention is paid to the opportunity of adopting so-called strength models and equations of state. Damage and failure modeling is discussed as well. In this part, specific interest is addressed to reviewing the so-called Johnson-Cook strength model, by critically highlighting its positive and negative aspects. One of the main tackled issue consists in a reasoned assessment of the various procedures adoptable in order to calibrate the parameters of the model. This phase is enriched and clarified by applying different calibration strategies to a real case, i.e. the evaluation of the model parameters for a structural steel. The consequences determined by each calibration approach are then carefully evaluated and compared. The second part of the work aims at introducing a new strength model, that consists in a generalization of the Johnson-Cook model. The motivations for the introduction of this model are first exposed and discussed. The features of the new strength model are then described. Afterwards, the various procedures adoptable for the determination of the material parameters are presented. The new strength model is then applied to a real case, i.e. a structural steel as above, and the results are compared to those obtained from the original Johnson-Cook model. Comparing to that, the obtained outcomes show that the new model displays a better capacity in reproducing experimental data. Results are discussed and commented. The third and final part of the work deals with an application of the studied topics to a real industrial case of interest. A device called perforating gun is analyzed in its structural problematics and critical aspects. This challenging application involves the modeling of several typologies of material, large strains, very high strain rate phenomena, high temperatures, explosions, hypervelocity impacts, damage, fracture and phase changes. In this regard, computational applications of the studied theories are presented and their outcomes are assessed and discussed. Several finite element techniques are considered. In particular, tridimensional Eulerian simulations are presented. The obtained results appear to be very promising in terms of the possibilities of a fruitful use in the design process of the device, in particular in order to achieve an optimization of its key features.

8 citations


Cites background or result from "Numerical modelling of ductile spal..."

  • ...(51) of the partial derivatives of the shear modulus with respect to the temperature, evaluated at the reference state....

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  • ...Furthermore, Cortes and Elices, 1995, provided experimental studies in aluminum, presenting also numerical modeling of spall fracture, showing good agreement between model predictions and experimental data....

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  • ...(49) and (51) with a simply melting model....

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  • ...s p G T   ∂ ∂ = + β ⋅ ε + ε ⋅ + ⋅ ⋅ + ⋅ ⋅ −     ∂ ∂ η   (51)...

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  • ...(49) and (51) by replacing the temperature with the internal energy, in order to make these equations more suitable for implementations in FEM codes or hydrocodes that operate with energy rather than temperature....

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Journal ArticleDOI
TL;DR: In this paper, the damage evolution and spall behavior of copper under complex shockwave loading conditions were investigated using plate impact experiments with conical targets, where sweeping tensile waves were generated by the interaction of the released waves that were reflected from the free surfaces of the impactor and the cone surface.
Abstract: The damage evolution and spall behavior of copper under complex shockwave loading conditions were investigated using plate impact experiments with conical targets. Sweeping tensile waves were generated by the interaction of the released waves that were reflected from the free surfaces of the impactor and the cone surface. From the free-surface velocity profiles measured by multi-channel velocimetry, the classic pull-back spall signals were observed in incipient and complete spallation experiments. The spall strength estimated from the pull-back velocity strongly depended on the loading path and the loading wave profile. Post-experiment analysis based on the soft-recovery technique revealed that the damage distributions were very different from the bottom to the top of the conical target, but the corresponding free-surface velocity data measured at different locations suggested that similar responses occurred, which indicated that the spall strength was the critical threshold stress of micro-void nucleation or early growth. The fractography analysis of the fracture surfaces showed that metal micro-spheres were scattered in deep dimples, which indicated that the increase in temperature due to local severe plastic deformation around the voids was important. With the same set of model parameters, the plate impact spallation experiments with plane and conical targets were simulated using a critical damage evolution model. A good agreement was obtained between the simulations and experiments, which demonstrated the model capabilities for predicting the spall responses of metals under complex shockwave loading.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigated the physical phenomena involved in the firing of a perforating gun in air at atmospheric pressure, by identifying all key factors stressing the gun carrier.
Abstract: Effective perforating gun firing constitutes a key process toward achieving safe and productive wells in hydrocarbon reservoir exploitation. Within this field, the present work pursues a novel modeling approach with two main aims: investigating the physical phenomena involved in the firing of a perforating gun in air at atmospheric pressure, by identifying all key factors stressing the gun carrier; assessing perforating gun performance dependence and optimization on the scallop geometry, in terms of the piercing capability of the carrier outcoming jets and of the gun carrier resistance. This is investigated through challenging 3D Eulerian FEM simulations, displaying coherence with key experimental evidences. The obtained results provide crucial information toward the understanding of the physical phenomena involved in gun firing and of the scallop geometry implications on gun performance. The present simulations set as an advanced tool for perforating gun design and optimization, in comparison with other methodologies like Lagrangian simulations or analytical modeling.

3 citations

Journal ArticleDOI
TL;DR: In this article , the authors report on finite deformation finite element calculations that analyze the response of porous ductile materials subjected to impact loading conditions and show that porosity in ductile material can, under certain circumstances, mitigate spall fracture by attenuating stress waves.
References
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Journal ArticleDOI
01 Jan 1950
TL;DR: In this article, a self-consistent method for the estimation of the shear modulus and the bulk modulus is proposed, where each hole is surrounded by a spherical shell of real material, and the reaction of the rest of the material is estimated by replacing it by equivalent homogeneous material.
Abstract: The effective bulk and shear moduli are calculated by a self-consistent method due to Frohlich and Sack. The bulk modulus k is determined by applying a hydrostatic pressure, and the shear modulus μ by applying a simple homogeneous shear stress, to a large sphere. Each hole is surrounded by a spherical shell of real material, and the reaction of the rest of the material is estimated by replacing it by equivalent homogeneous material For consistency, both the density and the displacement of the outer spherical boundary must be the same whether the hole and its surrounding shell are replaced by equivalent material or not. The effective elastic constants calculated from these conditions are 1/k = 1/k0ρ + 3(1 - ρ)/4μ0ρ + O[(1 - ρ)3], (μ0 - μ)/μ0 = 5(1 - ρ)(3k0 + 4μ0)/(9k0 + 8μ0) + O[(1 - ρ)2], where k0 and μ0 refer to the real material and ρ is the density of the actual material relative to that of the real material, in the next approximation k depends on the standard deviation of the volumes of the holes. The dilatation due to a distribution of pressures in the holes is p(1/k - 1/k0), where p is the mean obtained when the pressure in each hole has a weight proportional to the volume of the hole. By using the hydrodynamic analogue of the elastic problem, the theory is briefly applied to the theory of sintering, and used to discuss the effective viscosity of a liquid containing small air bubbles.

748 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a methodology that relates the kinetics of material failure on the microstructural level to continuum mechanics, by introducing micro-structural descriptions of damage into the continuum constitutive relations as internal state variables.

666 citations

Journal ArticleDOI
TL;DR: In this article, the collapse of a hollow sphere of incompressible elastic-plastic material, with appropriate pore radius and over-all porosity, has been analyzed.
Abstract: Static and dynamic pore‐collapse relations for ductile porous materials are obtained by analysis of the collapse of a hollow sphere of incompressible elastic‐plastic material, with appropriate pore radius and over‐all porosity. There are three phases of the pore‐collapse process: an initial phase, a transitional elastic‐plastic phase, and a plastic phase. The change in porosity during the first two phases is quite small. In the plastic phase, the static pore‐collapse relation is an exponential law that depends only on the yield strength of the material; the dynamic relation is a nonlinear second‐order ordinary differential equation that involves the yield strength and a material constant (with the physical dimension of time) that depends on the yield strength, the density, the initial porosity, and the pore radius. Comparison of the theoretical predictions with finite‐difference computer‐code calculations for pore collapse of a hollow sphere of compressible material indicates that the effect of elastic co...

556 citations

Journal ArticleDOI
TL;DR: In this paper, two conditions are proposed which place constraints on the processes of dynamic spall in condensed media, and determine inequalities which bound the spall strength, fragment size, and failure time.
Abstract: Two conditions are proposed which place constraints on the processes of dynamic spall in condensed media, and determine inequalities which bound the spall strength, fragment size, and failure time. Spall is defined as rupture within a body due to stress states in excess of the tensile strength of the material. The first is a horizon condition which establishes a domain of communication, consistent with the time to failure, within which spall must be independent of the surrounding environment. The second is an energy condition which requires that the potential and kinetic energy associated with the tensile loading process exceed the fracture energy of the material. Equality in the relations established from these conditions corresponds to energy-limited spall and provides specific analytic expressions for the spall properties. Inequality implies flaw-limited spall and requires more detailed material property information before spall can be characterized. Energy-limited spall is determined by the material fracture toughness in brittle solids and the material flow stress in ductile solids. Calculated spall properties, assuming energy-limited spall, compare well with experimental spall data for various materials. Under certain conditions, a transition from brittle to ductile spall (definition in text) with increasing strain rate is predicted. Comparison is made with spall data on 6061-T6 aluminum for which a brittle-to-ductile transition is predicted to occur at a critical strain rate of approximately 4 × 105 s−1. Energy-limited spall in liquids within their range of Newtonian fluid behavior is governed by surface energy and viscosity. Spall is predicted to be dominated by surface energy at low strain rates and viscous dissipation at high rates. Examples of each appear to exist within the scant experimental spall data available for liquids.

485 citations