Modeling of cavity coalescence during tensile deformation
Introduction
A number of materials undergo cavitation during hot plastic tensile deformation. The cavities nucleate at sites such as grain boundaries, second phase particles, and triple points; subsequently, they grow and interlink with neighboring cavities. Cavitation usually leads to premature tensile failure 1, 2. Examples of materials which are prone to cavitation include alloys of aluminum, copper, nickel, among others 3, 4, 5. Evidently, extensive cavitation usually imposes significant limitations on the commercial application of these materials.
The growth of isolated cavities within a specimen which is deforming under tensile loading conditions has been examined in some detail by several workers 6, 7. These efforts have led to the development of relations which describe the growth of an individual cavity as a result of plastic flow and/or diffusional mechanisms. However, these models typically do not account for cavity interlinkage (coalescence). Thus, they usually underpredict the average cavity size at a given degree of deformation.
Cavity coalescence was first modeled by Stowell et al. [8] and Pilling [9], who considered a distribution of “stationary”, randomly located cavities of various sizes which grow with strain. This theoretical analysis led to an expression which relates the average cavity radius to the individual (isolated) cavity growth rate and the temporal cavity volume fraction. Stowell et al.'s expression was later modified and simplified by Xinggang et al. [10], who also validated it to first order by comparing its predictions with experimental data.
In addition to the coalescence process per se, the influence of cavitation on overall tensile ductility has been examined in a number of macromechanical 11, 12 and micromechanical 13, 14 models. For example, early research on micromechanical modeling of cavitation processes assumed that the cavities form a symmetric network; a unit cell of the cavity network was utilized to study the deformation and cavitation process. These efforts focused on predicting the effects of the cavity growth rate, strain rate sensitivity, and cavity nucleation rate on tensile ductility, the final cavity volume fraction, and the failure mode. The effect of cavity coalescence was considered in only one of these studies [15]; however this work treated the phenomenon not mechanistically, but rather utilized Stowell et al.'s equation to account for cavity coalescence.
The objective of the present research was to model the cavity coalescence process within a tensile specimen through an analysis of (i) the temporal and spatial location of the cavities inside the specimen, and (ii) the temporal cavity radius. In contrast to earlier micromechanical models, a random cavity distribution inside the tensile specimen was considered to model the behavior of real materials. Outputs of the numerical analysis included predictions of average cavity radius, the fraction of cavities which coalesce, and the evolution of cavity size distribution.
Section snippets
Previous models
As mentioned in Section 1, the effect of coalescence on the apparent cavity growth rate was first described quantitatively by Stowell et al. [8] and Pilling [9], who derived an equation which predicts the variation of the average cavity radius r̄ with strain ε during uniaxial tensile deformation:in which Cv and η denote the cavity volume fraction and growth rate of an individual cavity, respectively, Φ(Δε)=[1+ηΔε/3+η2(Δε)2/27], Δε is an
Results and discussion
The principal outputs of the numerical model comprised predictions of average cavity radius, fractions of cavities which have coalesced, and cavity size distributions. The results presented below correspond to a fixed number of cavities (=40) for all values of cavity density and cavity growth rate η. However, in order to examine the influence of different cavity distributions and the number of cavities considered in the model on the coalescence results, a few simulations using different
Summary and conclusions
Cavity coalescence within specimens which undergo tensile deformation was investigated using a two-dimensional model developed in this research effort. The model takes into account the two strain-dependent effects of cavity growth and the change of the specimen dimensions which occur simultaneously during the process. The results of this study can be summarized as follows:
- 1.
There are two competing effects which govern the size of the ligament between two cavities and hence the occurrence of
Acknowledgements
This work was conducted as part of the in-house research activities of the Metals and Ceramics Division of the Air Force Research Laboratory, Materials and Manufacturing Directorate. One of the authors (P.D.N.) was supported under the auspices of the Air Force Contract No. F33615-96-C-5251.
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