R. Branco

A brief review of recent three-dimensional studies of brittle fracture

Abstract3D crack problems are area where a further intensive research is required. 3D solutions can shed more light on fracture and fatigue phenomena, provide a more accurate evaluation of strength and fatigue life or justify the application of the classical solutions of plane theories of elasticity. These, in fact, are approximate theories even when the governing equations of these theories are solved exactly. The current paper aims to provide a brief summary of the latest investigations of 3D effects associated with crack geometries and brittle fracture. In particular, we present an overview of the coupled fracture modes and 3D vertex singularities, which are currently largely ignored in experimental and theoretical studies. We also describe a recently developed experimental method for the evaluation of the stress intensity factors. This review is concerned with the situation generally described in the literature as small scale plasticity. Large plastic deformations and other non-linear effects are beyond the scope of this article.

A simplified method for the evaluation of fatigue crack front shapes under mode I loading

Two-dimensional elastic or elasto-plastic models dominate the current fatigue crack growth assessment and life prediction procedures for plate components with through-the-thickness cracks. However, as demonstrated in many theoretical and experimental papers, the stress field near the crack tip is always three-dimensional and, as a result, the fatigue crack front is not straight. It is normally curved towards the plate faces. Over the past few years there were a number of very careful numerical studies focusing on the evaluation of fatigue crack front shapes. However, the application of the direct numerical techniques to fatigue phenomena is a very tedious and time consuming process and, sometimes, it is quite ambiguous. In the current paper we develop a simplified method for the evaluation of the front shapes of through-the-thickness fatigue cracks. Further, we validate the developed method against experimental results, investigate the influence of various parameters on the crack front shapes at stable (steady-state) propagation and analyse the differences in the results of fatigue crack growth evaluation obtained with two- and three-dimensional approaches.

Extent of the Surface Region in Notched Middle Cracked Tension Specimens

This article aims at evaluating the extent of the surface region in notched Middle Cracked Tension specimens. Firstly, a fully automatic fatigue crack growth technique is developed to obtain stable crack shapes. After that, the stress triaxiality along the crack front is evaluated for different notch shapes. Then, objective criteria are defined to quantify the extent of the surface region from the stress triaxiality data collected. Next, the extent of the surface region is related to the elastic stress concentration factor of the uncracked geometry by a linear relationship. Finally, empirical two-constant equations able to evaluate the extent of the surface region from the thickness, notch radius, notch depth and elastic stress concentration factor are formulated.

Using a standard specimen for crack propagation under plain strain conditions

Purpose – Stress state has a major influence on different phenomena, namely those involving diffusion and plastic deformation (like crack closure and high‐temperature fatigue crack growth, void formation or ductile fracture). The isolation of plane stress and plane strain states is crucial in fundamental studies of material behavior. The isolation of plane stress state is achieved with thin specimens, whilst the isolation of plane strain state is usually done increasing the thickness or introducing lateral grooves. The purpose of this paper is to propose a specimen geometry able to isolate the plane strain state, based on the standard M(T) geometry.Design/methodology/approach – A numerical study was carried out aiming at obtaining a stress triaxiality parameter, h, as a function of different geometrical features of the specimen, such as the notch radius, notch depth and specimen thickness.Findings – Results show that a pure plane strain state is achievable (i.e. 97 percent of specimen thickness has h>0.97...

An encoderless high-performance synchronous reluctance motor drive

This paper presents an encoderless high-performance synchronous reluctance motor drive for traction applications. The control system is based on the active flux concept and a hybrid rotor position estimation algorithm is used, being this algorithm based on the injection of high-frequency signals at low speeds and on the position of the active flux vector for medium and high-speeds. A smooth transition algorithm between the two rotor position estimation methods is provided. Moreover, in order to improve the efficiency of the overall drive system, a loss minimization algorithm is proposed in order to reduce the motor copper losses when operating in steady-state. Experimental results obtained in the laboratory confirm the validity and adequacy of the proposed algorithms for the developed drive system.

Plasticity Induced Crack Closure under Plane Strain Conditions

Plasticity Induced Crack Closure (PICC) is a main phenomenon affecting fatigue crack growth and must be included in the design of components. The objective of the present paper is to study the level of PICC under plane strain conditions. The numerical parameters were identified and optimized. The effects of load level and material model were studied.

Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established.

A numerical study of non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, different authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle, were investigated. It was demonstrated that: i) LEFM concepts are applicable to the problem under study; ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; iii) the ?Keff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level; v) without contact there is no effect of stress ratio on crack tip parameters. Therefore it is proved that the crack closure concept is valid.

Influence of Material Parameters on Plasticity Induced Crack Closure

Plasticity Induced Crack Closure (PICC) is an important fatigue phenomenon affecting crack growth under cyclic loading, which makes important to consider it in the design of components. In this paper a parametric study that correlates elastic-plastic material parameters with plasticity induced crack closure (PICC) is presented. Yield stress and hardening coefficient were selected as the material parameters of interest and a sensitivity analysis was developed. The influence of the different parameters on PICC is explained based on the analysis of crack tip micromechanisms for plastic deformation.

Effect of numerical parameters on plastic CTOD

Fatigue crack growth (FCG) is associated with irreversible and non-linear processes happening at the crack tip. This explains different problems observed in the use of da/dN-?K curves, namely the inability to explain stress ratio and load history effects. The replacement of ?K by nonlinear crack tip parameters, namely the crack tip opening displacement (CTOD) is an interesting alternative. However, the determination of CTOD, using the finite element method, depends on different numerical parameters, not sufficiently studied so far. The objective here is to study the effect of these parameters on plastic CTOD, and therefore on da/dN-?CTODp curves. A transient behaviour was found at the beginning of numerical crack propagation which is linked to the formation of residual plastic wake. Therefore, a minimum number of crack increments is required to obtain stabilized values. On the other hand, the predicted ?CTODp decreases with the distance to crack tip. Close to the crack tip, sensitivity to the measured values is much higher, but it also exists at remote positions. In addition, the mesh has a relatively low influence on ?CTODp. Finally, the effect of the number of load cycles between crack increments greatly depends on material properties.