Fracture of brittle particles in a ductile matrix

Prerequisites for precipitate cracking in a yielding ductile matrix have been examined. A statistical model based on the fibre loading model combined with weakest link fracture theory is presented. With the model it is possible to estimate the effect of different variables on the particle fracture probability quantitatively. The predictions made are in excellent agreement with experimental results for a variety of different precipitate types. The result can be applied to calculate the probability of cleavage fracture for steels.

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Résumé On examine les conditions pour lesquelles un précipité fragile se rompt dans une matrice ductile en déformation plastique. On présente un modèle statistique basé sur les modèles de chargement d'une fibre et combiné avec la théorie de la rupture de la liaison la plus faible. Avec ce modèle, il est possible d'estimer quantitativement l'effet de diverses variables sur la probabilité de rupture d'une particule. Les prédictions qui sont avancées sont en excellent accord avec les résultats expérimentaux, pour une gamme de divers types de précipités. Les résultats peuvent être appliqués au calcul de la probabilité de rupture par clivage dans le cas des aciers.

     

Pull-out of a ductile fibre from a brittle matrix

The pull-out of a ductile fibre from a brittle matrix was analysed in Part I [1] using a shear-lag model. However, the analysis is formidable due to the consideration of Poisson's effect along the sliding length. This consideration is essential when the debonded fibre-matrix interface is subjected to Coulomb friction during fibre pull-out. To simplify the analysis, Poisson's effect is treated in an average sense in the present study, whereas it was treated pointwise in Part I. The present simplified solutions are in excellent agreement with the previous more rigorous and more complex solutions. The simplified model thus provides adequate solutions for the pull-out of a ductile fibre from a brittle matrix, and can be readily used for further applications.     

Pull-out of a ductile fibre from a brittle matrix

Pull-out of a ductile fibre from a brittle matrix has been analysed using a shear lag model. Debonding at the fibre-matrix interface and yielding of the fibre occurred during the pull-out process. Both Poisson's contraction of the fibre and Coulomb friction of the debonded interface were considered. The debond length, which consists of an elastic zone length and a plastic zone length, was also analysed. When the fibre has a finite embedded length, it was found that necking prior to full pull-out of the fibre was required to optimize the toughening of a brittle matrix due to plastic deformation of the fibres. The essential material properties to achieve this are addressed.     

Predicting whether a material is ductile or brittle

In this paper we discuss the various models that have been used to predict whether a material will tend to be ductile or brittle. The most widely used is the Pugh ratio, $G/K$, but we also examine the Cauchy pressure as defined by Pettifor, a combined criterion proposed by Niu, the Rice and Thomson model, the Rice model, and the Zhou-Carlsson-Thomson model. We argue that no simple model that works on the basis of simple relations of bulk polycrystalline properties can represent the failure mode of different materials, particularly where geometric effects occur, such as small sample sizes. Instead the processes of flow and fracture must be considered in detail for each material structure, in particular the effects of crystal structure on these processes.     

Overloads in ductile and brittle materials

The first part of the paper presents fatigue crack propagation experiments with single overloads at different overload ratios and specimen thickness in a very ductile austenitic steel. The results show that in the Paris regime in a ductile material, the overload effect can be explained solely in the framework of the change of the plasticity‐induced crack closure. Other effects such as strain hardening, blunting, additional damage, crack deflection and branching are not significant. Whether or not this behaviour can be observed in less ductile materials and also in the threshold regime is investigated in the second part. Periodic overload experiments were performed on a relatively ductile 2124, and a more brittle 359, particle‐reinforced aluminium alloy. In the Paris regime, the retardation in the 2124 reinforced alloy showed the expected behaviour for a ductile material, whereas in the 359 reinforced cast alloy, an acceleration of the mean growth rate was observed. Near the threshold the difference between the two alloys and the effect of the periodic overloads decreased.     

From brittle to ductile fracture of bone

Toughness is crucial to the structural function of bone. Usually, the toughness of a material is not just determined by its composition, but by the ability of its microstructure to dissipate deformation energy without propagation of the crack. Polymers are often able to dissipate energy by viscoplastic flow or the formation of non-connected microcracks. In ceramics, well-known toughening mechanisms are based on crack ligament bridging and crack deflection. Interestingly, all these phenomena were identified in bone, which is a composite of a fibrous polymer (collagen) and ceramic nanoparticles (carbonated hydroxyapatite). Here, we use controlled crack-extension experiments to explain the influence of fibre orientation on steering the various toughening mechanisms. We find that the fracture energy changes by two orders of magnitude depending on the collagen orientation, and the angle between collagen and crack propagation direction is decisive in switching between different toughening mechanisms.     

Discretized peridynamics for brittle and ductile solids

Peridynamics is a theory of continuum mechanics expressed in forms of integral equations rather than partial differential equations. In this paper, a peridynamics code is implemented using a graphics processing unit for highly parallel computation, and numerical studies are conducted to investigate the responses of brittle and ductile material models. Stress–strain behavior with different grid sizes and horizons is studied for a brittle material model. A comparison of stresses and strains between finite element analysis (FEA) and peridynamic solutions is performed for a ductile material. By applying the proposed procedure to bridge the material model defined for peridynamic bonds and the corresponding macroscale material model for FEA, peridynamics and FEA show good agreements as regards the stresses and strains. Copyright © 2011 John Wiley & Sons, Ltd.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Fracture mechanics of brittle matrix ductile fiber composites

A model to predict the increase in critical flaw size or stable crack growth potential which can occur by the inclusion of ductile fibers in a brittle matrix is considered. The model is based upon the super-position of two known stress intensity solutions; one for the crack opening mode resulting from a remotely applied stress and the second, an opposing stress intensity that results from a crack closing force exerted by unbroken fibers spanning the crack surfaces. The extent of stable growth possible is computed at the ultimate stress of the brittle phase as functions of fiber strength and of volume fraction for various amounts of fiber rupture. A hot pressed beryllium matrix is used as an example. The crack surface displacement over which a given fiber is capable of deforming without rupture is found to be sensitive to the fiber-matrix interface strength. The factors leading to maximum crack surface displacement without rupture are a high strain hardening capability of the fiber and an interface designed to fail at fiber stresses between yield and ultimate strengths.     

The debonding and pull-out of ductile wires from a brittle matrix

An experimental investigation into the debonding and pull-out of nickel wires from epoxy resin and cement paste matrices has been carried out. Above a critical embedded length both the debonding and pull-out stresses attain limiting values. A theory based on the model of a yielded zone travelling up the wire behind a debonding front was shown to describe the observed dependence of the limiting debonding stress on the yield stress, diameter and surface roughness of the wire. Pull-out behaviour subsequent to debonding was explained using this model in terms of an unyielded plug at the end of the wire. Orientation of the wire to the loading direction was found to raise the limiting debonding and pull-out stresses due to enhanced friction at the wire exit point.     

Impact modeling of foam cored sandwich plates with ductile or brittle faceplates

This paper reports numerical results of low velocity impact on open-face sandwich plates with an impactor of 2.65 kg mass hitting with 6.7 m/s velocity. The numerical simulation is done using 3D finite element models in LS-DYNA. The sandwich plates used for the present work have a core made of commercial aluminum alloy foam (Alporas) with faceplates made of either ductile aluminum (Al) or brittle carbon fiber reinforced plastic (CFRP). Selection of suitable constitutive models and erosion criterion for the failure analysis is investigated. A simplified analytical model for the peak load prediction under punch-through failure mode is presented. Numerically predicted contact force versus time, energy absorbed versus time along with the failure modes are compared with the experimental measurements and observations. Within experimental scatter, there is a good agreement between the numerical predictions and experimental measurements. Further more, the analytically predicted peak load values are in excellent agreement with the experimental measurements.     

Mechanisms of fatigue-crack propagation in ductile and brittle solids

The mechanisms of fatigue-crack propagation are examined with particular emphasis on the similarities and differences between cyclic crack growth in ductile materials, such as metals, and corresponding behavior in brittle materials, such as intermetallics and ceramics. This is achieved by considering the process of fatigue-crack growth as a mutual competition between intrinsic mechanisms of crack advance ahead of the crack tip (e.g., alternating crack-tip blunting and resharpening), which promote crack growth, and extrinsic mechanisms of crack-tip shielding behind the tip (e.g., crack closure and bridging), which impede it. The widely differing nature of these mechanisms in ductile and brittle materials and their specific dependence upon the alternating and maximum driving forces (e.g., ΔK andK _max) provide a useful distinction of the process of fatigue-crack propagation in different classes of materials; moreover, it provides a rationalization for the effect of such factors as load ratio and crack size. Finally, the differing susceptibility of ductile and brittle materials to cyclic degradation has broad implications for their potential structural application; this is briefly discussed with reference to lifetime prediction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Assessment of effect of ductile tearing on cleavage failure probability in ductile to brittle transition region

The fracture behaviour of ferritic and ferritic martensitic steels in ductile to brittle transition (DBT) region has been extensively studied in recent years and a probabilistic approach of master curve method is generally used to describe the fracture toughness of BCC steels in DBT region as a function of temperature. The assessment of cleavage failure probability however is still untouched in the upper region of ductile to brittle transition, although various extensions of master curve approach and various local approaches has been explored. Additionally the geometry and loading in tension and bending also adds up to the difficulties when cleavage failure is assisted with prior ductile tearing. In this work the cleavage fracture is investigated in upper region of DBT and a modified master curve approach is presented which can satisfactorily describe the fracture toughness as a function of temperature as well as amount of ductile tearing preceded by cleavage.