Roderick A. Smith

Finite element modelling of fatigue crack growth of surface cracked plates: Part II: Crack shape change

Abstract Investigations into the shape change of surface fatigue cracks are made by using the multiple degree of freedom model described in Part I. Three combinations of tension and bending loads are considered, i.e. DOB = 0 (pure tension), 0.5 and 1 (pure bending). Analyses of the shape of propagating crack fronts show that the semi-elliptical profile is approximately maintained during crack growth for all loading cases. Generally, the trend of aspect ratio changes predicted agrees with that from the Newman and Raju method for all three loading cases. However, for pure tension, as the crack closely approaches the plate back surface, a slight rise of aspect ratio was calculated, an effect which is absent in the predictions using the Newman and Raju method. The free boundary correction produces a slight effect on aspect ratio variations but seems to have extremely little influence on fatigue crack growth curves. The present predictions are in good agreement with limited experimental results on surface crack shape changes found in the literature.

Finite element modelling of fatigue crack growth of surface cracked plates: Part III: Stress intensity factor and fatigue crack growth life

Abstract Stress intensity factors (SIFs) and fatigue crack growth lives, obtained by a numerical simulation technique which is based on a multiple degree of freedom model, are presented. The results include those for both semi-elliptical static cracks and propagating cracks that are not necessarily semi-elliptical. Comparisons are made between the present results and the predictions from a two degree of freedom model based on the Newman and Raju closed-form SIF equation. The results show that the widely used Newman and Raju equation might be of relatively worse accuracy for cracks whose depth is larger than 90% of the plate thickness; that the present SIF predictions during crack growth are generally in good agreement with those obtained by the two degree of freedom method; and that most of the cracks approach, but cannot subsequently maintain, an iso-K profile because of the presence of both the front and back surfaces of the plate, or the bending component of the load. The free surface correction is also considered in both the multiple and two degree of freedom methods. The results show that the free boundary correction seems to have little influence on fatigue crack growth curves; and that agreement between the fatigue crack growth curves estimated from the present technique and the Newman and Raju ‘two-point plus semi-ellipse’ method, assuming the relation of CC=0.9mCA, is excellent for pure tension, while it becomes slightly worse for pure bending.

Stress intensity factors for corner cracks emanating from fastener holes under tension

Abstract In this paper, previous work associated with the stress intensity factor for corner cracks at fastener holes in finite thickness plates is briefly reviewed. The stress intensity factors for two symmetric quarter-elliptical corner cracks subjected to remote tension are evaluated by using both the quarter-point displacement and J-integral methods based on three-dimensional finite element analyses. The geometry ratios analyzed cover a wide range, i.e. depth ratio a/t: 0.2–0.95, aspect ratio a/c: 0.2–5, and hole radius ratio r/t: 0.5–3. Analysis of the J-integral path independence and mutual comparison of the stress intensity factor results between the two methods demonstrate that the present results are of good numerical accuracy. Deviation of the present results from some other solutions found in the literature is also revealed, particularly from Newman and Rajus equations. It is shown that the difference among these results obtained by the different methods is generally within a reasonable bound of error, but Newman and Rajus equations systematically underestimate (up to 15%) the stress intensity factor for cracks of depth ratio larger than 0.8.

Numerical analysis of fatigue growth of external surface cracks in pressurised cylinders

Fatigue crack growth is modelled by a novel numerical technique for various external surface cracks with initially either semi-elliptical or irregular crack fronts. The technique employs a three-dimensional finite element analysis to estimate the stress intensity factors at a set of points of the crack front, then calculates local crack advances by integrating a type of Paris fatigue crack growth law at this set of points, and finally establishes a new crack front and its corresponding finite element model. The multiple degrees-of-freedom model enables the crack shape to be predicted directly during crack growth without having to make the common semi-elliptical assumption, and therefore provides more accurate predictions. Fatigue analysis results are presented and discussed, including fatigue shape developments and deviations from the semi-elliptical shape, together with aspect ratio changes, stress intensity factor variations during crack growth and fatigue life predictions. Some of these results are also compared with those obtained by two simplified predictive methods based on one and two degrees-of-freedom models together with a stress linearisation.

FATIGUE SHAPE ANALYSIS FOR CORNER CRACKS AT FASTENER HOLES

Abstract Fatigue crack shape is simulated in this paper by a step-by-step finite element technique for corner cracks emanating from fastener holes in plates under cyclic tension loading. The numerical technique calculates the local growth increments at a set of points defining a crack front by employing a Paris type fatigue growth law, and permits the growth to be automatically advanced on a step-by-step basis. Hence, it can directly predict the shape development of propagating cracks. The fatigue shape analysis is concentrated on the growth simulation for several assumed initially quarter-elliptical corner cracks at three fastener holes of different hole radius. An initially irregular corner crack is also modelled to examine its shape development characteristic. The crack shape deviation from the widely-assumed quarter ellipse is numerically investigated by both the proposed relative residual and standard deviation criteria. The aspect ratio changes during crack growth are obtained and compared with limited experimental data found in the literature. Moreover, the influence of the power contained in the Paris law on the aspect ratio variation is studied.

A brief historical overview of the fatigue of railway axles

Abstract The history of railway axle design against fatigue is reviewed through a discussion of several notable accidents caused by broken axles. The earliest accidents prompted research into fatigue which resulted in a phenomenological understanding. In the last 50 years, largely through research directed towards the aircraft industry, fatigue has been recognized to be a process involving crack initiation and propagation. Fracture mechanics is now used to assist in the timing of crack inspection intervals, but a small number of failures still occur. The paper concludes with a short discussion of modern design methods, which have their origin in the nineteenth century. Some current pressures, particularly the need to reduce unsprung mass at high speeds, continue to challenge axle designers.

Railways: How they may contribute to a sustainable future

Abstract A combination of a rapidly increasing world population and an increasing energy-intensive lifestyle has led to doubts about the sufficiency of natural resources. The waste products of these economic activities have become large enough to change the climate of the globe. The demand for transport is characterized by an exponential increase and a tendency to choose faster modes. These facts give rise to concerns about the sustainability of present transport practices. While railways presently offer significant environmental advantages over other modes of transport, particularly the car, in many areas the gap is closing quickly. Cars are much safer, more energy efficient and less polluting than a decade ago. Trains in the future will have to contend with reducing hydrocarbon fuel supplies and much stricter legislation limiting emissions, particularly diesel particulates. Because the energy environmental performance of trains depends on the passenger load factor, the areas in which railways excel are high-speed intercity and commuting. Both these activities are well served by electric traction. With very few exceptions railway companies have not yet responded to significant environmental challenges. The oft-stated complacent view, that railways are environmentally superior to other modes of transport, fails to recognize that the competition is rapidly eroding their lead.

The Japanese Shinkansen: Catalyst for the Renaissance of Rail

This article outlines the history of railways in Japan and discusses the conditions leading to the bold decision to build a new type of line dedicated to high-speed passenger transport. Since opening of the high-speed Shinkansen line in 1964, speeds, frequency, and loadings have increased markedly, encouraging the development of similar systems in other countries. It is doubtful whether such schemes would have materialized without the Japanese lead. Railways have now emerged from decline and are seen as able to make a vital contribution to meeting the growth in transport demand expected in the future.

Analysis of crush behaviours of a rail cab car and structural modifications for improved crashworthiness

Abstract In this paper, the authors present a crashworthiness assessment and suggestions for modification of a conventionally designed rail vehicle with a driving cab (cab car). The analytical approach, based on numerical analysis, consisted of two stages. Firstly, the crashworthiness of the cab car was assessed by simulating a collision between the cab car and a rigid wall. Then, after analysing structural weaknesses, the design of the cab car was modified and simulated again in the same scenario. It was found that downward bending is an intrinsic weakness in conventional rail vehicles and that jackknifing is a main form of failures in conventional rail vehicle components. The cab car, as modified by the authors, overcomes the original weaknesses and shows the desired progressive collapse behaviour in simulation. The conclusions have general relevance for other studies but more importantly, point to the need for a rethink of some aspects of rail vehicle design.

The management of fatigue crack growth in railway axles

Abstract Railway axles are safety-critical components. Designing failsafe mechanisms is very difficult and the safety of the component is determined though a good understanding of the structural integrity and through effective management policies. This article first reviews from a historical viewpoint the development of the design and management of railway axles and then outlines state-of-the-art methodologies to be employed in the successful management of railway axles. Advancements in fatigue fracture mechanics have permitted the development of statistical techniques that enhance the understanding of axle failures which occur relatively infrequently. Because of the extremely low number of in-service failures, there exists a possibility to modify the non-destructive testing (NDT) inspection regime. This will reduce the maintenance costs without compromising safety. It is also shown that the probability of failure of an axle is profoundly influenced by the probability of missing a large fatigue crack during an NDT inspection. This crack may be growing rapidly and failure will ensue before the next inspection. The sensitivity of NDT techniques to small cracks is less important since these cracks will be growing relatively slowly and are not a threat to the structural integrity of the axle.