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The influence of grain size distribution on ductile intergranular crack growth resistance is investigated using full-field microstructure-based finite element calculations and a simpler model based on discrete unit events and graph search. The finite element calculations are carried out for a plane strain slice with planar grains subjected to mode I small-scale yielding conditions. The finite element formulation accounts for finite deformations, and the constitutive relation models the loss of stress carrying capacity due to progressive void nucleation, growth, and coalescence. The discrete unit events are characterized by a set of finite element calculations for crack growth at a single-grain boundary junction. A directed graph of the connectivity of grain boundary junctions and the distances between them is used to create a directed graph in J-resistance space. For a specified grain boundary distribution, this enables crack growth resistance curves to be calculated for all possible crack paths. Crack growth resistance curves are calculated based on various path choice criteria and compared with the results of full-field finite element calculations of the initial boundary value problem. The effect of unimodal and bimodal grain size distributions on intergranular crack growth is considered. It is found that a significant increase in crack growth resistance is obtained if the difference in grain sizes in the bimodal grain size distribution is sufficiently large. [ABSTRACT FROM AUTHOR]

A model based on discrete unit events coupled with a graph search algorithm is developed to predict intergranular fracture. The model is based on two hypotheses: (i) the key unit event associated with intergranular crack propagation is the interaction of a grain boundary crack with a grain boundary segment located at an angle with the initial crack plane; and (ii) for a given crack path, the overall crack growth resistance can be calculated using the crack growth resistance of a collection of unit events. Next, using a directed graph containing the connectivity of grain boundary junctions and the distances between them, and crack deflection versus crack growth resistance data, a directed graph in the J-resistance space is created. This graph contains information on the crack growth resistance for all possible crack paths in a given grain microstructure. Various crack growth resistance curves are then calculated including those corresponding to: (i) a local resistance minimum; (ii) a global minimum; and (iii) for verification, a path specified by microstructure-based finite element calculations. The results show that the proposed method based on discrete unit events and graph search can predict the crack path and the crack growth resistance for cracks that propagate from one grain boundary junction to another. The proposed computationally inexpensive model can be used to design material microstructures with improved intergranular fracture resistance, and/or to assess the overall crack growth resistance of materials with a known distribution of grain morphology. [ABSTRACT FROM AUTHOR]

Bulk tungsten normally undergoes brittle fracture at ambient temperatures and has a brittle-to-ductile transition in the range 200–300 °C. This limits the use of tungsten for a host of applications. In general, the fracture mode of tungsten at ambient temperature is intergranular whereas at high temperatures it undergoes transgranular fracture. In this work the focus is on the influences of microstructure and temperature on three-point bend fracture of polycrystalline pure tungsten. The samples were processed by equal channel angular extrusion (ECAE) through a 90° die angle via route A in order to produce an elongated microstructure. The mechanical behavior of both unprocessed and processed materials was then characterized by three-point bending at temperatures ranging from −45 °C to 425 °C. The results show that a single ECAE extrusion (strain ~ 1.15) reduces the flexural toughness of the material and increases the brittle-to-ductile transition temperature, while two and four extrusions dramatically increase the flexural toughness with little effect on the transition temperature compared to that of the unprocessed material. The flexural toughness of the material subjected to four extrusions (strains exceeding 4.5) is more than 50 times greater than that of the unprocessed material at ambient temperature. This is mainly due to microstructural changes that increase the resistance to intergranular fracture, enhance plastic dissipation, and activate relatively high fracture toughness crack systems for transgranular fracture. The results show that substantial elongation of grains by deformation processing at a temperature near the brittle-to-ductile transition temperature is an effective method for improving the ambient temperature ductility and toughness of bulk polycrystalline tungsten. [ABSTRACT FROM AUTHOR]

The goal of this paper is to predict how the properties of the constituent phases and microstructure of dual phase steels (consisting of ferrite and martensite) influence their fracture resistance. We focus on two commercial low-carbon dual-phase (DP) steels with different ferrite/martensite phase volume fractions and properties. These steels exhibit similar flow behavior and tensile strength but different ductility. Our experimental observations show that the mechanism of ductile fracture in these two DP steels involves nucleation, growth and coalescence of micron scale voids. We thus employ microstructure-based finite element simulations to analyze the ductile fracture of these dual-phase steels. In the microstructure-based simulations, the individual phases of the DP steels are discretely modeled using elastic-viscoplastic constitutive relations for progressively cavitating solids. The flow behavior of the individual phases in both the steels are determined by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Chen et al. in Acta Mater 65:133–149, 2014) while the damage parameters are determined by void cell model calculations. We then determine microstructural effects on ductile fracture of these steels by analyzing a series of representative volume elements with varying volume fractions, flow and damage behaviors of the constituent phases. Our simulations predict qualitative features of the ductile fracture process in good agreement with experimental observations for both DP steels. A ‘virtual’ DP microstructure, constructed by varying the microstructural parameters in the commercial steels, is predicted to have strength and ductile fracture resistance that is superior to the two commercial DP steels. Our simulations provide guidelines for improving the ductile fracture resistance of DP steels. [ABSTRACT FROM AUTHOR]

Abstract: Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment. [Copyright &y& Elsevier]

Plane strain finite element calculations of mode I crack growth are carried out under small scale creep conditions with an imposed stress intensity factor that is a prescribed cyclic function of time. The finite deformation analyses are based on a constitutive relation that couples creep deformation and damage due to grain boundary cavitation including a simple model of the embrittling effect of solute (oxygen) diffusion along grain boundaries. Isothermal analyses are carried out for two sets of material and grain boundary parameters: (i) parameter values representative of HASTELLOY ® X; and (ii) parameter values representative of P91. A stronger detrimental effect of environmentally assisted grain boundary embrittlement is found for HASTELLOY ® X than for P91. For a fixed imposed stress intensity factor range the detrimental effect is found to increase with increased hold time for HASTALLOY ® X. The variation of the predicted cyclic crack growth rate with imposed stress intensity factor range is found to be in good quantitative agreement with experimental results in the literature for both HASTELLOY ® X and P91. Paris law behavior, i.e. the cyclic crack growth rate depending on the imposed stress intensity factor range raised to a power, emerges naturally in the calculations. Parametric studies show that the cyclic crack growth rate and the Paris law exponent are more sensitive to variations in the grain boundary diffusivity, the solute diffusivity and a parameter characterizing the environmental embrittling effect than to parameters characterizing the creep response of the undamaged material. Also, an explicit analytical expression is found that gives a very good fit to the computed dependence of the cyclic crack growth rate on the solute diffusivity. [ABSTRACT FROM AUTHOR]

The resistance of polycrystalline materials to intergranular fracture depends on the toughness of the interfaces between neighboring grains. Using finite element simulations on model, two-dimensional microstructures, we demonstrate that the steady-state crack growth resistance of a polycrystal that contains exclusively high toughness interfaces is suboptimal: its crack growth resistance may be increased by introducing a minority fraction of weak interfaces at random locations within the interface network. Furthermore, the weaker are these interfaces, the greater is their toughening effect. These weak interfaces toughen the material through crack deflection and branching, nucleation of secondary cracks, and inelastic dissipation within intact interfaces. Our findings suggest that fracture resistance-oriented material development should not aim to eliminate all weak interfaces, but rather judiciously incorporate a low fraction of them. [Display omitted] [ABSTRACT FROM AUTHOR]

Ductile fracture involving nucleation, growth and coalescence of microscale voids limits the performance, safety, reliability and manufacturability of a variety of metallic components and structures. This phenomenon is affected by length-scales induced by the geometry of deformation, loading conditions and microstructure of the material. For example, under uniaxial tension, dual-phase (DP) advanced high strength steel sheets exhibit similar flow response along rolling (RD) and transverse directions (TD) with ductility along RD being either equal to or greater than TD. However, the bendability of sheet specimens with bend axis parallel to RD is less than the bendability of sheet specimens with bend axis parallel to TD. The objective of this work is to model the interplay of length-scales induced by bending and microstructure on ductile fracture of DP steel sheets. To this end, microstructure-based finite element calculations of ductile fracture in DP steel sheets under bending have been carried out. In the calculations, DP microstructures in a bend specimen are discretely modeled. Our results show that the microscopic state of stress/strain, and hence, damage evolution in DP steel sheets under bending are highly heterogeneous. The extent to which length-scales induced by bending and DP microstructure affects crack nucleation and early stage crack growth is discussed. Parametric studies to quantify the effect of initial porosity, susceptibility to secondary void nucleation and energy dissipated in damage evolution prior to crack nucleation on the bendability of DP steel sheets have also been carried out. • Microstructure-based modeling of ductile fracture under bending is carried out. • Microstructure and material parameter effects on bend fracture are quantified. • Deformation response of DP steel under bending is independent of microstructure. • Fracture resistance of DP steel under bending depends significantly on microstructure. • Crack nucleation away from the center of the bend specimen improves the bendability. [ABSTRACT FROM AUTHOR]