I. C. Howard

A general method for coupling microstructural response with structural performance

The paper sets out the general principles of a method of coupling finite element for the representation of the structural response with array of cellular automata to encompass the associated microstructural behaviour. For the purpose of this paper, cellular automata is a discrete time–discrete space system consisting of cells which may take one of several states. The state of a cell depends on the states of the neighbouring cells as well as on some macroscopic field variables. The paper goes on to show how these principles can be used, by applying them to problems of oxide scale cracking and of dynamic recrystallization during the hot working of steel, and to the ductile-to-brittle transition in the fracture of ferritic steels.

Modelling Recrystallisation during Thermomechanical Processing Using CAFE

A common feature that stimulates modelling efforts across the various physical sciences is that complex microscopic behaviour underlies apparently simple macroscopic effects. Mathematical formulations attempt to capture the initial and evolving microstructural entities either implicitly or explicitly and link their effects to measurable macroscopic variables such as load or stress by averaging out any microscopic fluctuations. The implicit formulations that ignore the inherent spatial heterogeneity in the deforming domain form the basis of constitutive models for input to finite element (FE) systems. On the other hand, explicit formulations to capture and link microstructural entities rely on narrowing down the size of each finite element, thereby increasing the number of finite elements in the deforming domain, an effect accompanied by a rapid growth in computational time. The model described here, Cellular Automata based Finite Elements (CAFE), utilises the Cellular Automata technique to represent initial and evolving microstructural features (e.g., dislocation densities, grain sizes, etc.) in C-Mn steels at an appropriate length scale by linking the macro-scale process variables obtained using an overlying finite element mesh. Differences will be illustrated between single and two-pass hot rolling experiments.

A Single Specimen CTOA Test Method for Evaluating the Crack Tip Opening Angle in Gas Pipeline Steels

Failure information from recent full-scale burst experiments on modern TMCP gas pipeline steels having a yield strength level of 690MPa and higher has shown that the CTOA fracture criterion can be effectively used to predict the arrest/propagation behaviour of the pipe against possible axial ductile fractures. The use of CTOA as an alternative or an addition to the Charpy V-notch and DWTT fracture energy in pipelines is currently under review. A significant difficulty currently limiting the more extensive use of CTOA in pipeline assessment is its practical evaluation either in the real structure or in a laboratory scale test. Different combinations of experimental and finite element analyses have been proposed for the measurement of the CTOA of a material. Although most of these models are able to predict the CTOA effectively, their implementation requires extensive calibration processes using the test load-deflection data. The authors have recently developed a novel test technique for direct measurement of the steady state CTOA using a modified double cantilever beam geometry. The technique uses optical imaging to register the uniform deformation of a fine square grid scored on the sides of the specimen. The slope of the deformed gridlines near the crack tip is measured during crack growth from captured images. Its value is a representative of the material CTOA. This paper presents recent results from the implementation of the technique to determine the steady state CTOA (steady state in this work refers to regions of ductile crack growth where CTOA values are constant and independent of crack length) of API X80 and X100 grade gas pipeline steels. In each case the approach was able to produce large amounts of highly consistent CTOA data from both sides of the test sample even from a single specimen. This extensive data set allowed an evaluation of the variance of the stable CTOA as the crack grew through the microstructure. The test method generated a steady CTOA value of 11.1° for X80 and 8.5° for X100 steels tested, respectively.Copyright

Experimental Study of Thickness and Fatigue Precracking Influence on the CTOA Toughness Values of High Grade Gas Pipeline Steel

Recent experimental and computational studies have revealed that the CTOA fracture criterion has the potential to assess steady state ductile rupture resistance during large amounts of crack growth. One of the major difficulties currently limiting the more extensive use of CTOA is its practical estimation either on a real structure or in a laboratory scale test. The authors have recently developed a novel test technique for direct measurement of CTOA. It is a single CTOA test (SCT) method using a modified double cantilever beam (DCB) specimen. Photographic and video techniques are used to register the progression of the crack tip in real time on the faces of the DCB. The CTOA profile is estimated from the uniform variations of the slope of a reference fine mesh scored on the surface of the specimen. Its value is representative of the material CTOA. So far the method has been successfully tested on gas pipeline steels of grade API X80 and X100 and 6000 series aluminium alloy. In all tests, it generated large amounts of highly consistent CTOA data, even from a single test specimen. This paper describes recent results from the CTOA testing of X100 steel specimens with different ligament thicknesses in the range of 8 to 12 mm, equivalent to 42 to 63% of the original pipe wall thickness. In total 18 sets of CTOA test data were obtained from opposite sides of fractured specimens. Analysis of these showed that the CTOA values were thickness independent in the examined range. An average CTOA value of 8.5° was found for X100 steel in the steady state crack propagation phase. The development of slant fracture associated with the steady CTOA region was completed after an average crack growth of 1.3–2.7 times the specimen ligament thickness. The fatigue precracking resulted in a 10–23% drop in the initiation load depending on the gauge thickness of the specimen and the initial crack length.Copyright

Measurement and Analysis of Impact Test Data for X100 Pipeline Steel

Charpy upper shelf energy is widely used as a fracture controlling parameter to estimate the crack arrest/propagation performance of gas transportation pipeline steels. The measurement of this fracture criterion particularly for modern steels and its apportion into different components, i.e. fracture and non-related fracture energy, are of great importance for pipeline engineers. This paper presents the results of instrumented Charpy impact experiments on high-grade pipeline steel of grade X100. First, the instrumentation technique including the design and implementation of a strain gauge load-cell and the details of the data-recording scheme are reviewed. Next, the experimental data obtained from the Charpy impact machine so instrumented are presented and discussed. These include the test data from full and sub-sized Charpy V-notched specimens. The instrumented Charpy machine was able to capture the load history in full during the fracture process of the test specimens resulting in a smooth load-time response. This eliminated the need for filtering used in similar test techniques. From the recorded test data the hammer displacement, impact velocity and fracture energy were numerically calculated. The results showed that there was a significant drop in hammer velocity during the impact event. This resulted in a change in the fracture mode from dynamic to quasi-static which was more appreciable for full-size Charpy test samples. As a result, sub-sized specimens might be preferable for impact testing of this steel in order to guarantee the conditions of dynamic crack propagation in the specimen ligament. Accurate analysis of the instrumented impact test data showed that the ratio of crack initiation energy to propagation energy was around 30% for the X100 steel. It can be concluded that in impact testing of high-grade pipeline steel a significant portion of overall fracture energy is consumed in non-related fracture processes. This high fracture initiation energy should be accounted for if the current failure models are going to be used for toughness assessment of highstrength low-alloy gas pipeline steels.

Extending the Local Approach to Fracture: Methods for Direct Incorporation of Microstructural Effects Into Finite Element Models of Fracture

The Local Approach to fracture phenomena has been very successful in helping to transfer information derived from testing one geometry on a material (laboratory specimens) to the prediction of the crack growth performance of another (the structure). At least in its most pervasive manifestations, it depends upon constructing finite element models with a ruling element size that is appropriate for the physical scale of the dominant failure mechanism. Since these are primarily of the order of the material microstructure, there is a consequential very strong mesh gradient towards the region of Local Approach interest. When applied to structures of engineering interest, which can be large, the resultant finite element models become very big, sufficiently so that they cannot be run on many computers, if at all. When there is more than one material scale involved, the situation becomes impossible to resolve with conventional finite elements, except through the use of compromise local finite element sizes that blend the requirements from each micro-scale into a smeared cell at the finite element level. Such models have shown considerable success in predicting the performance of a range of components and structures by a number of research groups. Even so, the method is constrained by the excessive computational costs associated with modeling realistic structures, and by other concerns derived from its smearing of possibly incompatible underlying physical effects. CAFE modeling, the coupling of Cellular Automata at the microstructural scale(s) with finite elements that are scaled only for the strain gradients expected at the macro-scale in the structure, offers a way out of these potential problems. The structural level field quantities, held at the element Gauss points, are modified according to information coming from the Cellular Automata with which each Gauss point is associated. Suitable code representing fracture initiation and propagation at the micro-level generates changes incrementally to the Gauss point field variables, which are then brought to equilibrium by the FE modeler (whenever it is an implicit FE system). The method allows a natural representation of the multiple scale interactions typical of the fracture of low alloy steels in the transition region.Copyright

Effect of friction on deformation during rolling as revealed by embedded pin technique

Abstract The paper investigates the effects of friction on the heterogeneity of deformation during rolling through studies using plane strain (2D) and three-dimensional (3D) finite element models designed to simulate the deformation of the embedded pin inserts during rolling. Redundant work due to friction is defined as a path function along the arc of contact. Since deformation during rolling is profoundly influenced by the amount of redundant work, which depends on friction as a path function along the arc of contact, the study has focused especially on methods of representing these frictional effects. The friction studied has been in one of two classes: the coefficient of friction being constant or varying parabolically along the arc of contact. The results show that the values of shear stress and normal pressure along the arc of contact depend upon the friction profile. The magnitude of these frictional effects is revealed by the through thickness variation of the relative pin insert displacement. This displacement changes in the 3D model because transverse spread reduces the amount of displacement along the axial direction. Comparison of the simulations with experimental pin insert shapes shows close agreement between the predicted and experimental results, while revealing the direction of further work needed to provide suitable mechanics models to interpret experimental pin insert data.

Bond graph and finite element analyses of temperature distribution in a hot rolling process: A comparative study

Abstract During the process of hot rolling, a metal is given its final shape by plastically deforming the original stock. This paper shows how variables, specifically the temperature, at each point in the deformation zone can be modelled using a multielement bond graph approach. Low-carbon steel has been considered and the modelling is described for single-pass hot rolling. Surface and centre temperature distributions are shown, and simulation results are found to be in good agreement between the two modelling techniques of bond graphs and finite element analysis.

Measurement and modelling of the crack tip opening angle in a pipeline steel

Recent developments in the control of propagating ductile fractures in gas pipelines have proposed using the Crack Tip Opening Angle (CTOA) as a measure of fracture resistance. This is attractive as it can be related directly to the geometry of the fracturing pipe and also can be implemented easily in finite element models of the propagating fracture process. Current methods of determining CTOA in linepipe have been based on the standard DWTT specimen. This geometry often does not allow a fully slant fracture to develop, and is loaded in bending rather than tension. A novel specimen design has been developed to measure CTOA under quasi-static conditions and applied to a X80 (Grade 555) pipeline steel. The experimental work involved development of the design to ensure crack path stability. CTOA was obtained directly by measurement from video images. The CTOA values dropped from an initially high value to a steady state value of about 8 degrees when fully slant crack growth was achieved. This required crack growth over a distance of about 5 to 12 times the test section thickness. The crack growth was modeled numerically using the Gurson ductile void growth material model. The finite element modeling was able to qualitatively reproduce the crack path instability observed in practice, and the fall of CTOA from the initial high value to a steady state condition. Although further work is required to improve the modeling, the work carried out to date has demonstrated that there is the potential to apply damage mechanics methods to predict the laboratory specimen response and then to model the structural response.Copyright

Three-dimensional damage theory of crack growth in large centre-cracked panels using the element removal technique

Abstract The conventional use of continuum ductile damage mechanics in finite element analysis identifies the crack tip or crack front by some criterion which, on the basis of developing parameters, deems a certain region to be cracked. In the region deemed to be cracked there is thus only a reduction in stresses, which thereafter falls continually. This paper incorporates in the damage model for both two and three dimensions, a facility which enables elements to be ‘switched off’ ehind the predicted crack front so that the stresses there are zero. A three-dimensional finite element analysis using this element removal scheme is performed to predict the deformation of centre-cracked panels under uniaxial and equibiaxial loading and to study the applicability of this scheme.