Inelastic deformation of porous materials

doi:10.1016/0022-5096(89)90014-8

Journal of the Mechanics and Physics of Solids

Volume 37, Issue 6, 1989, Pages 693-715

https://doi.org/10.1016/0022-5096(89)90014-8 Get rights and content

Abstract

This paper examines the structure of material constitutive laws for time-independent plastic and creeping porous bodies through the determination of bounds to the flow and strain-rate potentials. The results are a logical extension of conventional plasticity and creep formalisms for incompressible materials. It is demonstrated that the shape of the yield surface for a time-independent plastic material and the surface of constant energy dissipation rate for a creeping solid are a function of stress and void volume fraction only, and independent of material parameters apart from a weak dependence on the creep exponent, n. This condition is not satisfied by the model proposed by Gurson (J. Engng Mater. Tech. Trans. ASME, 99, 2, 1977) and modifications are suggested to his model and its extension to material hardening. The predictions obtained for a creeping solid are in broad agreement with results of other studies.

References (21)

B. Budiansky et al.
Mechanics of Solids, The Rodney Hill 60th Anniversary Volume
J.M. Duva
Mech. Mater.
(1986)
J.M. Duva et al.
Mech. Mater.
(1984)
G.H. Edward et al.
Acta Metall.
(1979)
K. Hellan
Int. J. Mech. Sci.
(1975)
R. Hill
J. Mech. Phys. Solids
(1967)
F.A. Leckie et al.
Acta Metall.
(1977)
N. Ohno et al.
J. Mech. Phys. Solids
(1984)
J.R. Rice et al.
J. Mech. Phys. Solids
(1969)
M.F. Ashby et al.
Creep Damage Mechanics and Mechanisms
Natn. Phys. Lab. U.K. Rep. DMA(A) 77
(1984)

There are more references available in the full text version of this article.

Cited by (144)

Coupling a void growth model with an elastoplastic material model for a simultaneous prediction of the borehole plastic zone and critical collapse pressure
2024, Geoenergy Science and Engineering
The elastoplastic shear stability of an inclined borehole is explored in this study. Unlike other previously published elastoplastic wellbore stability solutions, this work considered the contributions of the anti-plane shear stresses. A new framework for estimating the critical elastoplastic collapse pressure and the extent of the plastic zone around the borehole is presented. In this approach an elastoplastic material model is coupled with a void-growth model to simultaneously predict the collapse pressure and plastic zone. In this paper, the Gurson void-growth model is coupled with an elastic-brittle plastic material model, and the critical collapse mudweight and plastic radius at the orientation of maximum compression are solved simultaneously from the resulting system of equations. The predicted collapse mudweights from the proposed approach compared very well with observed field data. When compared with the conventional method (NYZA = 1), the proposed framework performed better, although the difference can be negligible in some cases.
Pressure assisted sintering stress exponent assessment methods: Accuracy analysis and effect of sintering stress
2023, Mechanics of Materials
Pressure assisted sintering models involve creep based mechanisms having different stress exponent values. The later evolve from linear viscous diffusional creep mechanisms to highly non-linear mechanisms involving dislocation motion. Consequently, the determination of the stress exponent is of key importance to define the sintering mechanisms and one of the first parameters to identify for the assessment of sintering model. Different methods exist in the literature involving tests at different pressures or with a stepwise pressure profile to extract the creep stress sensitivity. Open questions remain on the accuracy of these methods with the impact of sintering stress (high in ceramics nano-powders) or transient microstructure evolution for the stepwise approaches. This accuracy issue is investigated on an alumina submicronic powder by comparing different methods based on sinter-forging and Spark Plasma Sintering (SPS) at 1200 °C. We show that the sintering stress has a high influence on the identified value of stress exponent. Otherwise, the combination of sintering stress and transient behavior at the level of the pressure “jump” of the stepwise method can lead to high disturbance in the identified values.
A new experimental and simulation methodology for prediction of recrystallization in Ni-based single crystal superalloys during investment casting
2022, Journal of Materials Processing Technology
A new methodology involving both experimentation and modeling to predict the recrystallization of nickel-based single-crystal superalloy parts after subsequent heat treatment is presented. Anisothermal mechanical tests are used to provide further validation of a thermal-elasto-viscoplastic behavior model, and process-specific values of the thermal expansion coefficient. Critical test specimens are casted, and modeled to monitor the thermal-mechanical histories of interesting zones. The proposed model is capable of predicting higher plasticity locations, consistently with the occurrence of recrystallization. Critical plasticity paths for recrystallization are identified, defining three regions: unrecrystallized, transition and recrystallized zones. Phenomenological-based numerical plastic strain and energy criteria for AM1 single-crystal superalloy are built, and validated on an industrial case. The proposed methodology provides a systematic approach for part design and process parameters optimization, enabling recrystallization to be predicted and hence avoided.
A porosity-based model of dynamic compaction in under-dense materials
2022, International Journal of Solids and Structures
Citation Excerpt :
Cocks and Ashby (1980) developed a porosity evolution expression assuming a strain-rate dependent material. General viscoplastic potentials for porous strain-rate dependent materials were subsequently developed in Duva and Hutchinson (1984), Cocks (1989), Michel and Suquet (1992), Duva and Crow (1992) and Sofronis and McMeeking (1992). These potentials were then linked to porosity evolution expressions (such as that of Cocks and Ashby) in Marin and McDowell (1996) and Moore (2018).
Under-dense metals including micro-architectured structures and stochastic foams provide a combination of low weight, high strength-to-weight ratio, high permeability, and low stiffness, which make them desirable materials for a variety of applications. Specifically, their energy absorption capabilities under dynamic compressive loads are desirable. However, under high loading rates there are several challenges in performing accurate simulations of under-dense materials—primarily, the responses of materials with high, low, and zero porosity are difficult to accurately predict with a single model. A general model that tracks porosity and pore geometry and is flexible for a variety of matrix material constitutive responses has yet to be produced. This work outlines such a model and applies it to high loading rate simulations that demonstrate the model’s ability to address a variety of stress states. The approach is to extend a porosity model meant for isolated porosity of low-to-modest volume fraction to the application space of under-dense materials. Calibration parameters are used to account for complex mechanisms as well as the effects of the geometries of various under-dense materials. This results in a general, versatile, and flexible model. A study of the model’s sensitivity to calibration parameters is shown along with qualitative and quantitative comparisons to direct numerical simulations (DNS) and predictions resulting from impact velocities and flyer structures for which the model is not calibrated. This model can simulate a range of compaction conditions and is less computationally intense than direct numerical simulations which gives it utility in the design of micro-architected materials for impact mitigation, energy absorption, and other applications.
Porous stage assessment of pressure assisted sintering modeling parameters: a ceramic identification method insensitive to final stage grain growth disturbance
2021, Acta Materialia
Pressure assisted sintering models such as Skorohod-Olevsky's, Abouaf's or Riedel's require the identification of at least four parameters depending on porosity or temperature. The identification of these parameters is difficult at high temperature and for high pressures because of the non-linear mechanical behavior which makes them closely interconnected. To solve this problem, the fully dense behavior is identified first allowing determining the porous behavior afterward. This typical approach is well employed for metal or viscous materials. However, for ceramics the final stage grain growth makes the fully dense mechanical tests irrelevant; because the equivalent dense phase behavior of sintered specimens has bigger grains (then longer diffusion distances) than in initial/intermediate stages of sintering. Consequently, most of the parameters of these ceramics models compensate the dense parameters overestimation by an underestimation in the porous parameters values. In this paper we propose a unique formulation based on sinter-forging and die compaction which directly identify all the parameters from the porous stage. This comprehensive determination is possible by a non-reductive hypothesis on the shear modulus function shape and the experimental determination of radial/vertical displacement on sinter-forging tests. Such an approach allows an instantaneous determination of the parameters insensitive from the actual grain size of the porous ceramic.
Thermomechanical model for solidification and cooling simulation of Ni-based superalloy components
2021, International Journal of Solids and Structures
One of the challenges encountered in the industrialization of new single-crystal superalloys parts (like high-pressure turbine blades and vanes for aircraft engines) is to limit the mechanical stresses during the solidification and cooling of the metal. In order to accurately predict the viscoplastic flow as well as the thermo-mechanical behaviour of Ni-based superalloy during its cooling, in this study a thermodynamically-consistent thermo-elasto-viscoplastic model was developed. This model takes into account the solid-liquid transition occurring in the material during the cooling phase. This is done by introducing a compressible-type viscoplastic yield function based on appropriate equivalent stress depending on volume fraction of the solid phase formed by the propagation of dendrites inside the liquid phase of the material. This model was implemented in Abaqus/Standard© F.E. code and applied to the identification of material parameters of Ni-based superalloy using isothermal tensile-relaxation tests driven for different strain rates and temperatures. First, anisothermal tensile-compression test was simulated on a single integration point. A comparison of the experimental and numerical stress-strain response partially validate the model. Second, a benchmark test involving casting of a rectangular Ni-based superalloy bar in a sand mold was simulated and analyzed.

View all citing articles on Scopus

View full text

Inelastic deformation of porous materials

Abstract

Mech. Mater.

Mech. Mater.

Acta Metall.

Int. J. Mech. Sci.

J. Mech. Phys. Solids

Acta Metall.

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Creep Damage Mechanics and Mechanisms

Natn. Phys. Lab. U.K. Rep. DMA(A) 77