تاثیرات میکرو ساختاری بر روی شکست انعطاف پذیر در مواد ناهمگن. تجزیه و تحلیل حساسیت با LE-VCFEM: قسمت اول

Ductile failure of heterogeneous materials, such as cast aluminum alloys and discretely reinforced aluminums or DRA’s, initiates with cracking, fragmentation or interface separation of inclusions, that is followed by propagation in the matrix by a ductile mechanism of void nucleation and growth. Damage localizes in bands of intense plastic deformation between inclusions and coalesces into a macroscopic crack leading to overall failure. Ductile fracture is very sensitive to the local variations of the microstructure morphology. This is the first of a two part paper on the effect of microstructural morphology and properties on the ductile fracture in heterogeneous ductile materials. In this paper the locally enhanced Voronoi cell finite element method (LE-VCFEM) for rate-dependent porous elastic–viscoplastic materials is used to investigate the sensitivity of strain to failure to loading rates, microstructural morphology and material properties. A model is also proposed for strain to failure, incorporating the effects of important morphological parameters.

Ductile failure in metals and alloys containing heterogeneities such as particulates, fibers or precipitates, generally initiates at the heterogeneity with fragmentation or interface separation. Subsequently, the microstructural damage propagates into the matrix by mechanisms of void growth. Often, the damage localizes in bands of intense plastic deformation between heterogeneities, which subsequently coalesce into macroscopic cracks leading to complete failure. Experimental studies on ductile failure have shown strong connections between the microstructural morphology and damage nucleation and growth. A robust understanding of the influence of the microstructure on ductile fracture is essential for material design. A variety of experimental studies have been undertaken on the influence of morphology on ductile failure, particularly related to cast aluminum alloys and DRA’s [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and [12]. In their studies on cast aluminum alloys, Caceres et al. [13], [14], [6], [15], [16] and [17] have shown that ductility of the Al–7%Si–0.4%Mg cast alloy depends on both the dendrite cell size and the size and shape of silicon inclusions. While these experimental studies offer good qualitative understanding, they do not quantify the influence of microstructure parameters on ductile fracture. Often, the difficulty arises with isolating the effect of individual morphological parameters like shape, size or spatial distribution [15]. Analytical and computational models have been implemented for fulfilling this need. Computational studies have been conducted to study elastic–plastic deformation and ductile failure of heterogeneous materials in [18], [19], [20], [21], [22], [23] and [24]. A majority of these are unit cell models with size scales exceeding 1 μm, that use continuum micromechanics for modeling inclusions and matrix [25]. There is a paucity of image-based models that consider aspects of the real microstructural morphology, such as non-uniformities in inclusion shape, size, orientation and spatial distribution. The predictive capability of unit cell models for failure properties is very limited due to over-simplification of the microstructure. Quite often, critical local features necessary to model strain to failure are lost in these models. Ductile fracture depends strongly on the extreme values of microstructural characteristics, e.g. nearest neighbor distances, highest local volume/area fraction, etc. and computational models must feature some of these characteristics for accuracy. Additionally, many of the existing studies have focused only on the initial stages of ductile damage, e.g. crack nucleation in the inclusions, and have not considered evolution of ductile failure by matrix void growth and coalescence. Computational models developed by Ghosh et al. [26], [27], [28], [29], [30], [31] and [32] have focused on more realistic representation of microstructures with non-uniform dispersion of heterogeneities. The microstructural Voronoi cell finite element model or VCFEM by Ghosh et. al. [26], [27], [28], [29], [30] and [31] offers significant promise for accurate micromechanical analysis of arbitrary heterogeneous microstructures with high efficiency. Morphological non-uniformities in dispersions, shapes and sizes, obtained from micrographs are readily modeled by this method [33]. This method has been extended in the locally enhanced VCFEM (LE-VCFEM) [32] to model ductile fracture in heterogeneous microstructures. In LE-VCFEM, the stress-based hybrid VCFEM formulation is adaptively enhanced in regions of localized plastic flow to model stages of ductile fracture, from inclusion fragmentation to matrix cracking in the form of void nucleation, growth and coalescence. These regions are overlaid with finite deformation, displacement-based elements to accommodate strain softening in the constitutive behavior. LE-VCFEM has been demonstrated to be quite effective for simulating ductile fracture in [32]. This is the first of a two part paper on the effect of microstructural morphology and properties on ductile fracture in heterogeneous materials. In this part, extensive sensitivity studies are conducted with results of LE-VCFEM based micromechanical analyses of rate-dependent porous elastic–viscoplastic materials, to quantify the effects of loading rates, microstructural morphology and material properties on strain to failure. Based on the sensitivity study, a model is proposed for strain to failure, incorporating the effects of important morphological parameters. The 2D locally enhanced VCFEM is extended to rate-dependent porous elastic–viscoplastic materials in Section 2. In Section 3, sensitivity analyses with LE-VCFEM simulations are used to study the quantitative effect of applied strain rate, inclusion volume fraction, size, shape, orientation and spatial dispersion, as well as material properties on ductile fracture.

In this first of a two part paper on ductile fracture in heterogeneous materials, extensive microstructure based sensitivity studies are conducted to quantify the effects of loading rates, microstructural morphology and material properties on strain to failure. The locally enhanced VCFEM (LE-VCFEM) for rate-dependent porous elastic–viscoplastic materials is used for two-dimension micromechanical analyses of rate-dependent ductile fracture. The strain to failure is governed by damage nucleation due to inclusion cracking that is followed by damage propagation by void nucleation, growth and coalescence in the matrix. This is readily simulated by LE-VCFEM with good accuracy and efficiency. Strain to failure is found to be very sensitive to the loading rate, microstructure morphology, and material properties of the matrix and inclusions. High applied strain rates result in early cracking of inclusions. For a uniform material with a single inclusion in the microstructural domain, this leads to an increase of strain to failure due to redistribution of micro-stresses in the matrix and inclusion. This causes a delay in plastic response and a reduction in void evolution rate in the neighborhood of the crack. However, this inference cannot be generalized to more complex microstructures, in which early cracking may have different influence on the overall ductile behavior. Strain to failure of heterogeneous alloys is very sensitive to the inclusion morphology and orientation. Large inclusions of high aspect ratio that are oriented along the loading axis are ideal sites for damage nucleation. The exponential and power law correlations found between strain to failure and inclusion aspect ratio and size respectively delineate this strong sensitivity. On the other hand, damage growth and coalescence in the matrix is affected by the spatial distribution of inclusions rather than by their morphology. Microstructural domains with high levels of clustering have significantly lower strain to failure than those with uniform inclusion distribution. An asymptotic correlation between strain to failure and clustering is found from the sensitivity analysis. This implies a reduction in sensitivity with increasing level of clustering. Based on the sensitivity study, a model is proposed for strain to failure, incorporating the effects of clustering, volume fraction, orientation, shape, size and orientation of inclusions. The sensitivity analysis also shows that the matrix yield stress and the inclusions failure strength are important determinants of ductility. An increase in the matrix yield stress leads to an increase of the maximum tensile stress that is accompanied by a much lower ductility. The matrix work-hardening exponent on the other hand does not have much effect on ductility for the microstructure and material properties considered in this work. Additionally, strain to failure is found to be very sensitive to the failure strength of inclusions. It is important that a material designer considers both microstructural morphology and material properties in optimizing ductility. In part 2 of this paper, the model for strain to failure developed in part 1 is used to successfully predict strain to failure of actual microstructures taken from micrographs of an aluminum alloy A356.