Alojz Ivankovic

Cohesive zone models and the plastically deforming peel test

The peel test is a popular test method for measuring the peeling energy between flexible laminates. However, when plastic deformation occurs in the peel arm(s) the determination of the true adhesive fracture energy, G c , from the measured peel load is far from straightforward. Two different methods of approaching this problem have been reported in recently published papers, namely: (a) a simple linear-elastic stiffness approach, and (b) a critical, limiting maximum stress, σ max , approach. In the present article, these approaches will be explored and contrasted. Our aims include trying to identify the physical meaning, if any, of the parameter σ max and deciding which is the better approach for defining fracture when suitable definitive experiments are undertaken. Cohesive zone models Fracture mechanics Laminates Peel tests Plastic deformation

Mechanical characterisation of polyurethane elastomer for biomedical applications

Mechanical testing and modelling of a material for biomedical applications have to be based on conditions representative of the application of interest. In this work, an ether-based polyurethane elastomer is used to build mock arteries. The aim is to study the behaviour of arteries under pulsatile loading conditions and how that behaviour changes with the development and progression of atherosclerosis. Polyurethane elastomers are widely used as biomaterials, e.g. in tube form for bypasses and catheters. However, their mechanical behaviour has not been extensively characterised. This work establishes the variations in the behaviour of polyurethane elastomer with temperature, humidity and strain rate and also reports planar and equibiaxial tension, relaxation, creep and cyclic test results, providing a comprehensive characterisation of the material. Test results are used to determine the properties of the polyurethane elastomer and in the selection of a representative material model for future simulations of arterial behaviour and the development of atherosclerosis. The results show that the behaviour of the elastomer is significantly dependent on both humidity and temperature, with Youngs modulus of 7.4 MPa, 5.3 MPa and 4.7 MPa under dry-room temperature, wet-room temperature and wet at 37 ( composite function)C conditions, respectively. The elastomer also exhibits rate-dependent viscoelastic behaviour. Yeohs hyperelastic material model provided the best fit to the entire range of experimental data. The Neo-Hookean model provides a good fit at small strain but significantly diverges at large strains. Nevertheless, in applications where deformations are relatively small, i.e. below 15%, the Neo-Hookean model can be used.

Application of the finite volume method to the analysis of dynamic fracture problems

A detailed description of a new numerical method for the solution of dynamic fracture problems is presented. The method employs finite volume discretization of the equilibrium equations.The present work considers the analysis of rapid crack propagation (RCP) in two-dimensional geometries only. The simulation of steady-state RCP in a peeling-strip geometry, and an economical approach which allows the calculation of the crack driving force from a ‘snapshot’ computation of the displacement field are described. Also presented is the modelling of transient RCP in single edge notch tensile specimens, based on a fixed-mesh ‘node release’ technique and a ‘holding back’ force concept. It is shown that finite volume results are in very good agreement with both analytical and finite element predictions. The accuracy, simplicity and efficiency of this novel method are also demonstrated.

Crack growth predictions in polyethylene using measured traction¿separation curves

Abstract The accuracy of predicting the crack growth in any cohesive zone model calculation depends critically on the choice of cohesive law. A novel experimental method was used to measure directly such a cohesive law or ‘traction–separation curve’ in polyethylene. Deep notched tensile specimens were tested under constant displacement rate conditions, which facilitated a localisation of the damage mechanisms thought to precede crack growth and allowed a quantification of these processes independent of bulk deformation. Results showed that both the fracture energy and cohesive strength measured in this manner are a function of the applied rate and specimen geometry. Here we present a cohesive zone model within the finite-volume method to predict crack initiation and propagation history in three grades of polyethylene of different toughness, using the experimental measurements described above. The choice of cohesive law is crucial as it has a fundamental bearing on the predicted crack growth rates, particularly in tough polymers, where changes in the prevailing rate, constraint and temperature may affect the magnitude of the holding tractions within the damage zone. Initially a single experimentally measured, fixed rate traction–separation curve was used in the model as the fracture criterion but was unable to provide satisfactory crack growth predictions. By contrast, use of a more physically realistic family of curves measured at different rates provided better agreement of the prediction with experiment for the tough polyethylenes and very good agreement for the more brittle polyethylene. It was concluded that along with a rate dependent cohesive law, an accurate prediction of the crack growth history of tough polyethylenes would also require an incorporation of the effects of variations in constraint and perhaps also temperature. The ultimate goal may therefore be the development of a physical material model, sufficiently calibrated by experimental data, which would be able to accurately describe the local fracture process via a rate, constraint and temperature dependent traction–separation law.

Validation of a fluid–structure interaction numerical model for predicting flow transients in arteries

Fluid-structure interaction (FSI) numerical models are now widely used in predicting blood flow transients. This is because of the importance of the interaction between the flowing blood and the deforming arterial wall to blood flow behaviour. Unfortunately, most of these FSI models lack rigorous validation and, thus, cannot guarantee the accuracy of their predictions. This paper presents the comprehensive validation of a two-way coupled FSI numerical model, developed to predict flow transients in compliant conduits such as arteries. The model is validated using analytical solutions and experiments conducted on polyurethane mock artery. Flow parameters such as pressure and axial stress (and precursor) wave speeds, wall deformations and oscillating frequency, fluid velocity and Poisson coupling effects, were used as the basis of this validation. Results show very good comparison between numerical predictions, analytical solutions and experimental data. The agreement between the three approaches is generally over 95%. The model also shows accurate prediction of Poisson coupling effects in unsteady flows through flexible pipes, which up to this stage have only being predicted analytically. Therefore, this numerical model can accurately predict flow transients in compliant vessels such as arteries.

FINITE-VOLUME APPROACH TO THERMOVISCOELASTICITY

ABSTRACT This article presents a development of the finite-volume method for solving linear thermoviscoelastic deformation problems. Hereditary continuum problems represented by spatially elliptic second-order partial differential equations with memory are considered. This is motivated by the need to develop numerical algorithms for the solution of thermoviscoelastic stress analysis problems, although it is expected that results presented will generalize to other Volterra problems. Assuming that the hydrostatic and deviatoric responses are uncoupled, and using the temperature–time equivalence hypothesis, the constitutive equations are expressed in an incremental form. Procedures for analyzing linear viscoelastic deformation are described, and numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms. The accuracy of the method is demonstrated through comparison with analytical and experimental results as well as with numerical solutions obtained elsewhere.

A finite-element analysis study of the metatarsophalangeal joint of the hallux rigidus

Hallux rigidus was first described in 1887. Many aetiological factors have been postulated, but none has been supported by scientific evidence. We have examined the static and dynamic imbalances in the first metatarsophalangeal joint which we postulated could be the cause of this condition. We performed a finite-element analysis study on a male subject and calculated a mathematical model of the joint when subjected to both normal and abnormal physiological loads. The results gave statistically significant evidence for an increase in tension of the plantar fascia as the cause of abnormal stress on the articular cartilage rather than mismatch of the articular surfaces or subclinical muscle contractures. Our study indicated a clinical potential cause of hallux rigidus and challenged the many aetiological theories. It could influence the choice of surgical procedure for the treatment of early grades of hallux rigidus.

Stress Wave Propagation Effects in Split Hopkinson Pressure Bar Tests

Studies of the properties of materials at high strain rates by the split Hopkinson pressure bar suggest that most materials show a sharp increase in strain rate sensitivity at high rates. In this paper, analytical and numerical evidence is presented which shows that his apparent increase in the strain rate sensitivity reported in the literature may result from stress wave propagation effects present in the test. A one-dimensional analytical solution has been developed for a rate independent bi-linear material tested in a split Hopkinson pressure bar apparatus. The solution, which is based on a stress wave reverberation model, shows that there is an apparent increase in the strain rate sensitivity of the material which can only be explained in terms of large propagating plastic wave fronts in the specimen. Numerical modelling of the same test geometry for the same input material model is in excellent agreement showing conclusively that stress wave propagation effects are inevitable at high impact velocities. The assumption of uniform stress and strain distribution within a split Hopkinson pressure bar specimen is therefore incorrect at high impact velocities. The formulation of the novel numerical code used in the present work, which is based on the finite volume technique, is also presented.

Cohesive zone modelling of crack growth in polymers Part 2 –Numerical simulation of crack growth

Abstract Cohesive zone models, which incorporate some form of cohesive law as the fracture criterion within the localised damage zone, are increasingly being used in the fracture assessment of tough engineering materials. However, the exact characterisation of the material within the damage zone is crucial as it has a fundamental bearing on the computed crack growth rates. A procedure is presented for implementing a cohesive zone model using the finite volume method by incorporating experimentally measured traction curves as the local fracture criterion. Experimental load–time and crack growth data in tough polyethylene for a three point bend geometry are compared with numerical predictions. Reasonable agreement is achieved between experiment and model predictions when a single fixed rate traction–separation curve is used for all cells along the prescribed crack path. Predictions are improved by incorporating a scheme for switching between a family of rate dependent curves in place of a single fixed rate curve. Results also indicate the necessity of incorporating the effect of difference in constraint along the crack path into the choice of the local traction–separation law.

A local modulus analysis of rapid crack propagation in polymers

This work is concerned with the analysis of rapid crack propagation (RCP) in Polymethylmethacrylate (PMMA), Polycarbonate (PC) and two-layer PMMA/PC systems. Remarkably constant crack speeds were observed, and higher crack speeds corresponded to the higher preloads. Uniform fracture surfaces were associated with these constant speed RCPs. An indirect method was used to characterise dynamic fracture properties of the materials. The method relies on the recorded crack length histories and boundary conditions which are incorporated in a dynamic Finite Element (FE) code to generate the crack resistance (GID). The numerical simulation of the constant speed RCPs generated highly scattered GID data. Very large variations of the computed GID with the crack length did not correspond to fracture surface appearances. Geometry dependent and multivalued crack resistance results with respect to the crack speed cast doubt on the uniqueness of GID. In this work, attempts were made to overcome these difficulties by exploring the concept that the anomalies arise from large local strains around the rapidly moving crack tip, resulting in the crack ‘seeing’ a low local modulus. It is demonstrated that the critical source of error on the analysis of RCP, is the improper linear elastic representation of the material behaviour around the propagating crack tip. Since the parameters describing the behaviour of the materials near the propagating crack tip were unknown, local non-linear effects were approximated by a local low modulus strip along the prospective crack path. The choice of the local modulus was justified by measurements of the strain histories along the crack path during RCP. The local strip low modulus model generated a larger amount of the kinetic energy in the sample and the crack resistance was reduced compared to results from the single constant modulus approach. Most importantly, GID data were nearly independent of the crack length, crack speed and the specimen size. This local modulus concept was also successfully applied to the analysis of RCP in the duplex specimen configuration.