N.P. O'Dowd

Gradient-dependent deformation of two-phase single crystals

Abstract In this work, a gradient- and rate-dependent crystallographic formulation is proposed to investigate the macroscopic behaviour of two-phase single crystals. The slip-system-based constitutive formulation relies on strain-gradient concepts to account for the additional strengthening mechanism associated with the deformation gradients within a single crystal with a high volume fraction of dispersed inclusions. The resulting total slip resistance in each active system is assumed to be due to a mixed population of forest obstacles arising from both statistically stored and geometrically necessary dislocations. The non-local theory is implemented numerically into the finite element method and used to investigate the effect of the relevant microstructural (i.e., size and volume fraction of precipitated inclusions) and deformation-gradient-related length scales on the macroscopic behaviour of a typical nickel-based superalloy single crystal. An analytical framework to link the strain-gradient effects at the microscopic level with the macroscopic behaviour of an equivalent homogeneous single crystal is also proposed.

Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains

Abstract This work describes the finite element implementation of a generalised strain gradient and rate-dependent crystallographic formulation for finite strains and general anisothermal conditions based on a multiplicative decomposition of the deformation gradient. The implementation involved the development of both a novel finite element formulation to determine the spatial slip rate gradients at each material point, and an implicit numerical integration scheme at the constitutive level to update the stresses and solution dependent variables. The time-integration procedure uses a Newton–Raphson scheme with a single level of iteration to solve the incremental non-linear equations associated with the non-local constitutive formulation. Closed-form solutions for the relevant fourth-order Jacobian tensors are given. The proposed numerical scheme is formulated in a general form and hence should be applicable to most existing crystallographic models. The crystallographic formulation is then used to investigate the effect of the morphology and volume fraction of the reinforcing phase of a two-phase single crystal on its macroscopic behaviour.

Use of scaling functions to determine mechanical properties of thin coatings from microindentation tests

The indentation of elastic‐plastic coatings deposited on elastic substrates is studied in this work. The functional expressions that relate the load‐indentation behaviour to coating and substrate material properties are derived using dimensional analysis in conjunction with finite element simulations. Based on these scaling functions, a method is proposed to determine the coating Young’s modulus, yield strength and strain hardening properties from the microindentation tests. A method to obtain improved estimates of the material hardness is also discussed. While the analyses are based on a conical (i.e. Rockwell) indenter, the indenter angle used in the simulations was selected so that the results can also be used to extract mechanical properties from measurements using the pyramidal indenters such as Vickers and Berkovich types. ” 2000 Elsevier Science Ltd. All rights reserved.

Fracture mechanics analysis of a crack in a residual stress field

The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.

Creep crack growth prediction using a damage based approach

This paper presents a numerical study of creep crack growth in a fracture mechanics specimen. The material properties used are representative of a carbon-manganese steel at 360 o C and the constitutive behaviour of the steel is described by a power law creep model. A damage-based approach is used to predict the crack propagation rate in a compact tension specimen and the data are correlated against an independently determined C* parameter. Elastic-creep and elastic-plastic-creep analyses are performed using two different crack growth criteria to predict crack extension under plane stress and plane strain conditions. The plane strain crack growth rate predicted from the numerical analysis is found to be less conservative than the plane strain upper bound of an existing ductility exhaustion model, for values of C* within the limits of the present creep crack growth testing standards. At low values of C* the predicted plane stress and plane strain crack growth rates differ by a factor between 5 and 30 depending on the creep ductility of the material. However, at higher loads and C* values, the plane strain crack growth rates, predicted using an elastic-plastic-creep material response, approach those for plane stress. These results are consistent with experimental data for the material and suggest that purely elastic-creep modelling is unrealistic for the carbon-manganese steel as plastic strains are significant at relevant loading levels.

Determination of the mechanical properties of metallic thin films and substrates from indentation tests

Abstract A procedure to obtain the elasto-plastic mechanical properties of strain-hardening materials from indentation tests, based on dimensional analysis and finite-element techniques, is proposed. The method is applicable to homogeneous materials and to coatings deposited on substrates of known mechanical properties. The Youngs modulus of the material is extracted from the initial slope of the unloading indentation curve and the yield strength and strain- hardening exponent are obtained from the maximum indentation load and the contact area after unloading. The method is used to obtain the properties of a high-alloy steel and Mo and AlSi coatings deposited on a steel substrate by plasma spraying. The sensitivity of the measurement to the depth of indentation is discussed.

Experimental Evaluation of the J or C * Parameter for a Range of Cracked Geometries

In the current ASTM Standard Test Method for Measurement of Creep Crack Growth Rates in Metals (E 1457) the experimental C* parameter is related to the load and creep load line displacement rate through the geometry related η factor. In this work η factors for a range of geometries are presented. The geometries examined are the compact tension specimen, C(T), single edge notch specimen in tension, SEN(T), and bending, SEN(B), double edge notch specimen in tension, DEN(T), middle crack specimen in tension, M(T) and the C-shaped specimen in tension CS(T). Calculations have been performed for a linear elastic-power law hardening material but the resulting η factors are applicable to either power law plastic or power law creeping materials. Values for ηLLD and ηCMOD, based on the load line displacement and crack mouth opening displacement, respectively, have been determined. A wide range of crack depths, 0.1⩽a/W⩽0.7, where a is crack length and W is specimen width, and hardening exponents, 3 ⩽N ⩽10, under plane stress and plane strain conditions have been examined using the finite element method. The influence of specimen length, crack length, material properties and out of plane stress state on the η factor has also been considered. It has been found that for shallow cracks the value of η depends quite strongly on the exponent, N in the material power law, regardless of whether η is defined based on the load line displacement or crack mouth opening displacement. The ηLLD factor has also been found to be strongly sensitive to plane stress/strain conditions imposed, a/W and specimen length, whereas ηCMOD depends more weakly on a/W and is almost independent of specimen length for the cases examined. There is, however, no clear trend in these variations over the range of specimen geometries and a/W examined. These results are found to be consistent with those in the literature. Recommendations are made regarding the most appropriate values for η, depending on the specimen type and geometry while taking into account the variability due to the material properties, out of plane stress state and variations between the numerical analyses.

Weibull stress solutions for 2-D cracks in elastic and elastic-plastic materials

The Weibull stress is widely used as a measure of the probability of cleavage failure. In this work analytical and semi-analytical expressions for the Weibull stress are developed in terms of the remote loading parameters, J or K, and material properties. Results are presented for sharp cracks and notches in elastic and elastic-plastic materials under plane stress and plane strain conditions. The proposed relations enable Weibull stress estimates to be obtained without the need for costly finite element analyses and provide insight into the use of the Weibull stress as a parameter for the prediction of cleavage failure of cracked bodies. The expressions have been verified using finite element techniques and good agreement has been found throughout. The results of the analyses have been used to interpret the mesh size dependence of Weibull stress values obtained from finite element calculations.

Measurement of residual stresses in T-plate weldments

Tensile welding residual stresses can, in combination with operating stresses, lead to premature failure of components by fatigue and/or fracture. It is therefore important that welding residual stresses are accounted for in design and assessment of engineering components and structures. In this work residual stress distributions, obtained from measurements on a number of ferritic steel T-plate weldments using the neutron diffraction technique and the deep-hole drilling method, are presented. It has been found that the residual stress distributions for three different plate sizes are of similar shape when distances are normalized by plate thickness. It has also been found that the conservatisms in residual stress profiles recommended in current fracture mechanics-based safety assessment procedures can be significant—of yield strength magnitude in certain cases. Based on the data presented here a new, less-conservative transverse residual stress upper bound distribution is proposed for the T-plate weldment geometry. The extent of the plastic zone developed during the welding process has also been estimated by use of Vickers hardness and neutron diffraction measurements. It has been found that the measured plastic zone sizes are considerably smaller than those predicted by existing methods. The implications of the use of the plastic zone size as an indicator of the residual stress distributions are discussed.

Numerical study of sliding wear caused by a loaded pin on a rotating disc

Abstract A computational approach is proposed to predict the sliding wear caused by a loaded spherical pin contacting a rotating disc, a condition typical of the so-called pin-on-disc test widely used in tribological studies. The proposed framework relies on the understanding that, when the pin contacts and slides on the disc, a predominantly plane strain region exists at the centre of the disc wear track. The wear rate in this plane strain region can therefore be determined from a two dimensional idealisation of the contact problem, reducing the need for computationally expensive three dimensional contact analyses. Periodic unit cell techniques are used in conjunction with a ratchetting-based failure criterion to predict the wear rate in the central plane strain region. The overall three dimensional wear rate of the disc is then determined by scaling the plane strain wear rate with a conversion factor related to the predicted shape of the wear track. The approach is used to predict pin-on-disc test data from an Al–Si coating using a tungsten carbide pin. The predicted results are found to be consistent with measured data.