Eine Übergangsbedingung beim Strahlverschleiß von Gesteinen und Betonen

A transition criterion for the erosion of rocks and concrete materials Depending on loading regime and material type, mineralic materials behave either elastic or elastic‐plastic if eroded by solid particles. A simple transition number, X, that combines fracture toughness and compressive strength, can be used to distinguish between both modes. Conventionally ‘hard’ materials, namely granite and feldspars, own low X‐values and respond elastic. Conventionally ‘soft’ material, namely limestone, mortar and schist, are characterised by high X‐values and show an elastic‐plastic response.     

Mechanical Behavior of Multilayered Nanoscale Metal‐Ceramic Composites

Single and multilayered structures at nano‐length scale are very attractive materials due to their high strength, toughness, and wear resistance relative to conventional laminated composites. In this study, single layered Al, SiC, and multilayered Al/SiC composites were synthesized by DC/RF magnetron sputtering. The microstructure of the multilayered structures was characterized by scanning electron microscopy (SEM). The elastic and plastic behavior of single and multilayered materials was investigated by nanoindentation and tensile testing. For nanoindentation, an analytical model was employed to subtract the contribution of the Si substrate, in order to extract the true modulus of the films. Finite element simulations were employed to confirm the analytical predictions and to investigate the anisotropic elastic behavior of the multilayered composite. It was concluded that while indentation provides reasonable Young's modulus and hardness values in monolithic layers, it does not provide the true modulus of the multilayered materials because of their inherent anisotropy.     

Buckling of Carbon/Glass Composite Tubes Under Uniform External Hydrostatic Pressure

Abstract: This paper describes an experimental and an analytical investigation into the collapse of 44 circular cylindrical composite tubes under external hydrostatic pressure. The results for 22 of these tubes were from a previous investigation and the results for a further 22 models are reported for the first time in this paper. The investigations concentrated on fibre‐reinforced plastic tube specimens made from a mixture of three carbon and two E‐glass fibre layers. The lay‐up was 0°/90°/0°/90°/0; the carbon fibres were laid lengthwise (0°) and the E‐glass fibres circumferentially (90°). The theoretical investigations were carried out using a simple solution for isotropic materials, namely a well‐known formula by ‘von Mises’. The previous investigation also used a numerical solution based on ANSYS, but this was found to be rather disappointing. The experimental investigations showed that the composite specimens behaved similarly to isotropic materials previously tested, in that the short vessels collapsed through axisymmetric deformation while the longer tubes collapsed through non‐symmetric bifurcation buckling. Furthermore, it was discovered that the specimens failed at changes of the composite lay‐up due to the manufacturing process of these specimens. These changes seem to be the weak points of the specimens. For the theoretical investigations, two different types of material properties were used to analyse the composite. These were calculated properties derived from the properties of the single layers given by the manufacturer and also the experimentally obtained properties. Two different approaches were chosen for the investigation of the theoretical buckling pressures, of the previously analysed models, namely a program called ‘MisesNP’, based on a well‐known formula by von Mises for single‐layer isotropic materials, and two finite element analyses using the famous computer package called ‘ANSYS’. These latter analyses simulated the composite with a single‐layer orthotrophic element (Shell93) and also with a multi‐layer element (Shell99). The results from Shell93 and Shell99 agreed with each other but, in general, their predictions were higher than the analytical solution by von Mises. The von Mises solution agreed better than the finite element solutions for the longer vessels, which collapsed by elastic instability, particularly when the experimentally obtained material properties were used. Thus, it was concluded that the results obtained from the finite element analyses predicted ‘questionable’ buckling pressures. The report provides design charts by all approaches and material types, which allow the possibility of obtaining a ‘plastic knockdown factor’ for these vessels. The theoretical buckling pressures obtained using the computer programs MisesNP or ANSYS can then be divided by the plastic knockdown factor obtained from the design charts, to give the predicted buckling pressures. It is not known whether or not this method can be used for the design of very large vessels.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Influence of contact geometry on hardness behavior in nano-indentation

In this paper the influence of contact geometry, including the round tip of the indenter and the roughness of the specimen, on hardness behavior for elastic-plastic materials is studied by means of finite element simulation. We idealize the actual indenter by an equivalent rigid conic indenter fitted smoothly with a spherical tip and examine the interaction of this indenter with both a flat surface and a rough surface. In the latter case the rough surface is represented by either a single spherical asperity or a dent (cavity). Indented solids include elastic perfectly plastic materials and strain hardening elastic–plastic materials, and the effects of the yield stress and strain hardening index are explored. Our results show that due to the finite curvature of the indenter tip the hardness versus indentation depth curve rises or drops (depending on the material properties of the indented solids) as the indentation depth decreases, in qualitative agreement with experimental results. Surface asperities and dents of curvature comparable to that of the indenter tip can appreciably modify the hardness value at small indentation depth. Their effects would appear as random variation in hardness.     

A low-cycle fatigue life prediction model of ultrafine-grained metals

A (high strain) low‐cycle fatigue (LCF) life prediction model of ultrafine‐grained (UFG) metals has been proposed. The microstructure of a UFG metal is treated as a two‐phase ‘composite’ consisting of the ‘soft’ matrix (all the grain interiors) and the ‘hard’ reinforcement (all the grain boundaries). The dislocation strengthening of the grain interiors is considered as the major strengthening mechanism in the case of UFG metals. The proposed model is based upon the assumption that there is a fatigue‐damaged zone ahead of the crack tip within which the actual degradation of the UFG metal takes place. In high‐strain LCF conditions, the fatigue‐damaged zone is described as the region in which the local cyclic stress level approaches the ultimate tensile strength of the UFG metal, with the plastic strain localization caused by a dislocation sliding‐off process within it. The fatigue crack growth rate is directly correlated to the range of the crack‐tip opening displacement. The empirical Coffin–Manson and Basquin relationships are derived theoretically and compared with experimental fatigue data obtained on UFG copper (99.99%) at room temperature under both strain and stress control. Good agreement is found between the model and the experimental data. It is remarkable that, although the model is essentially formulated for high strains (LCF), it is also found to be applicable at low strains in the high‐cycle fatigue (HCF) regime.     

Direct analysis of elastic–plastic structures with ‘overlay’ materials during cyclic loading

Several computer codes have incorporated the ‘overlay’ material models: the volume element, which is characteristic of the material, is composed of sub-elements with different kinematic hardening, perfectly plastic or even viscoplastic flow rules and different elastic properties, these sub-elements exhibiting all, however, the same total strain.¹,² In this paper it is demonstrated how the simple mathematical framework we first proposed for elastic-plastic structures with kinematic hardening material,³ and we extended to some elastic viscoplastic ones,⁴ can easily be applied to these particular ‘overlay’ materials. One of the interesting advantages of this approach is a straightforward analysis of structural response under cyclic loadings by applying the linear elastic analysis.     

Structural integrity of pipelines: T-stress by line-spring

The elastic T‐stress is an important constraint parameter for characterizing elastic–plastic crack‐tip fields and in fracture assessment procedures. However, many of the methods reported in the literature for estimating T‐stress are not easily suited for surface‐cracked pipes because these are three‐dimensional in nature. Here, the line‐spring method is demonstrated to be an efficient and accurate tool for the constraint estimation in surface‐cracked pipes. Detailed three‐dimensional analyses are performed to verify the line‐spring results. Using the line‐spring method, the effects of different crack geometries and diameter‐to‐thickness ratio on stress‐intensity factor (SIF) and T‐stress in circumferentially surface‐cracked pipes are examined. Further, a compendium of normalised SIF and T‐stress values for surface‐cracked pipes in remote tension and bending, calculated from a total of 1000 analyses, is tabulated. Finally, the application of an ‘elastic–plastic’ T‐stress under large‐scale plasticity is explored.     

Nonlinear mode III crack stress fields for materials obeying a modified Ramberg‐Osgood law

In this paper, an analytical study is carried out on the work‐hardening, elastic‐plastic stress distributions in a cracked body under antiplane shear deformation. A modified Ramberg‐Osgood law is introduced to describe the material behaviour, and stress and strain fields are derived in closed form. Compared with the conventional Ramberg‐Osgood formulation, the new law includes the effect of a new parameter, κ, which allows the transition from the ideally elastic behaviour (low stress regime) to the power law behaviour (large stress regime) to be controlled, thus providing 1 more degree of freedom to better fit the actual behaviour of engineering materials. A discussion is carried out on the features of stresses and strains close to and far away from the crack tip.     

Three‐dimensional mixed‐mode (I and II) crack‐front fields in ductile thin plates — effects of T‐stress

It has been well‐established that the non‐singular T‐stress provides a first‐order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic–plastic crack‐front field under mode I loading conditions. The objective of this paper is to exam the T‐stress effect on three‐dimensional (3D) crack‐front fields under mixed‐mode (modes I and II) loading. To this end, detailed 3D small strain, elastic–plastic simulations are carried out using a 3D boundary layer (small‐scale yielding) formulation. Characteristics of near crack‐front fields are investigated for a wide range of T‐stresses (T/σ₀ = ?0.8, ?0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters M_e = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T‐stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T‐stress. It is important to include these effects when investigating the mixed‐mode ductile fracture failure process in thin‐walled structural components.     

A rate‐consistent and intrinsically path‐dependent incremental method for plastic buckling problems

This paper presents an incremental predictor–corrector method which is able to handle the continuous spreading of elastic unloading and, therefore, is particularly well suited to solve plastic bucking problems. The method, which deals explicitly with rate variables and equations, is (i) rate consistent, because it leads to the ‘true’ tangent matrix, and (ii) intrinsically path‐dependent, because it enables an adequate identification and characterization of the onset of elastic unloading within each incremental step. Copyright © 2000 John Wiley & Sons, Ltd.     

Dissimilar Friction Stir Welding Between 5083 and 6082 Al Alloys Reinforced With TiC Nanoparticles

Dissimilar friction stir welding between aluminum alloys thick plates reinforced with TiC nanoparticles was conducted. The defect-free welds are characterized by good mechanical mixing between the joined materials as well as by good nanoparticle distribution and further grain refinement in comparison with the unreinforced weld. The local mechanical behavior of the produced metal matrix composites was studied and compared with their bulk counterparts and parent materials. Specifically, the measured mechanical properties in microscale and nanoscale (namely hardness and elastic modulus) are correlated with microstructure and the presence of fillers. The hardness, elastic modulus, ultimate tensile strength, percentage of elongation, and yield values increase with the presence of TiC nanoparticles.     

Viscoplastic plane‐strain analysis of infinite solids using elastic supports

A highly efficient novel Finite Element Boundary Element Method (FEBEM) is proposed for the elasto‐viscoplastic plane‐strain analysis of displacements and stresses in infinite solids. The proposed method takes advantage of both the Finite Element Method (FEM) and the Boundary Element Method (BEM) to achieve higher efficiency and accuracy by using the concept of elastic supports to simulate the effects of unbounded solid mass surrounding the region of interest. The BEM is used to compute the stiffnesses of elastic supports and to estimate the location of the truncation boundary for the finite element model. As compared to the conventional coupled FEBEM, the proposed method has three main computational advantages. Firstly, the symmetrical and highly banded form of the standard finite element stiffness matrix is not disturbed. Secondly, the proposed technique may be implemented simply by using standard codes for elasto‐viscoplastic finite element analysis and elastic boundary element analysis. Thirdly, the yielded zone is approximately located in advance by using the BEM and hence, an unnecessarily large extent of the domain does not have to be discretized for the finite element modelling. The efficiency and accuracy of the proposed method are demonstrated by computing elastic and elasto‐plastic displacements and stresses around ‘deep’ underground openings in rock mass subject to hydrostatic and non‐hydrostatic in situ stresses. Results obtained by the proposed method are compared with ‘exact’ solutions and with those obtained by using a BEM and a coupled FEBEM. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of Wooden Board Strength Class on the Performance of Cross‐laminated Timber Plates Investigated by Means of Full‐field Deformation Measurements

Although cross‐laminated timber (CLT) plates are increasingly used in high‐performance building structures, a tailored composition of them or, at least, a performance‐based classification scheme is not available. Especially, the influence of the quality of the ‘raw’ material (wooden boards) on the load carrying capacity of CLT elements is hardly investigated yet. For this reason, within this work, bending tests on 24 CLT plates consisting of wooden boards from three different strength classes have been carried out. The global mechanical response as well as the formation of failure mechanisms were investigated, including a full‐field deformation measurement system, which allowed for a qualitatively as well as quantitatively identification of board failure modes. Interestingly, no influence of the board strength class on the elastic limit load of the CLT plates was observed, but the situation was different for the load displacement history beyond the elastic regime, where basically, two different global failure mechanisms could be distinguished. The obtained knowledge about the ‘post‐elastic’ behaviour of CLT plates may serve as a basis for the optimisation of CLT products and the development or improvement of design concepts, respectively. Moreover, the obtained large ‘post‐elastic’ capacity reserve of CLT consisting of high quality boards could lead to a better utilisation of the raw material.     

Mechanical properties and hardness of boron and boron-rich solids

A brief review of the recent studies of the crystal and electronic structure and its stability under large strain-shear and tensile deformation of selected boron compounds, which have been predicted to be superhard on the basis of their high elastic moduli, is presented. It will be shown that in many cases, the materials undergo electronic instability and transformation to softer phases with a lower shear resistance than the original equilibrium structure. Therefore, high values of elastic moduli (“low compressibility”) do not guarantee high hardness. These results also challenge the recent “models of theoretical hardness of an ideal crystal”, which are based on the equilibrium electronic properties. It is shown that appropriately nanostructured materials open the way to the design of superhard materials.     

Strahlverschleiß von Stahl mit niedrigem Kohlenstoffgehalt: Untersuchungen zur Verschleißpartikelgeometrie

Erosion of low‐carbon steel by solid particle impingement: aspects of wear debris geometry Image analysis software was used to analyse the geometry of debris formed during the erosion of low‐carbon steel by impinging solid particles. Depending on the two‐dimensional aspect ratio (ratio between debris height and debris width), three different debris types could be distinguished. The most frequent type observed was a platelet‐type debris as suggested by the Bellman‐Levy (1981) model. This wear debris shape type covered about 60 % of all acquired debris. Plain micro‐machining according to Finnie’s (1959) suggestion played a negligible role only, but other processes, namely ploughing as suggested by Winter and Hutchings (1974), were more important. The statistically estimated mean debris size was about 14 μm. About 92 % of all wear debris had sizes smaller than the target material grain size. This result supports the figure that multi‐step removal modes – the formation and detachment of lip or platelet from crater rims ‐ were responsible for material removal.     

An estimation of true Ramberg‐Osgood curve parameters for materials with and without Luder's strain using yield and ultimate strengths

Engineering tensile stress–strain curves for metallic materials typically show two different behaviours, namely, with Luder's strain and without Luder's strain. Luder's strain is more common for ductile materials, whereas high‐strength steels deform without Luder's strain. Usually, the stress–strain curves of ductile steels exhibit ultimate load where necking starts to develop. On the other hand, steels with low ductility exhibit monotonic increase of the applied load till failure without necking. Recently, Kamaya proposed a method to estimate the Ramberg‐Osgood relationship parameters for true stress–strain curves on the basis of conventional yield and ultimate strengths. This method can be not accurate enough for ductile materials exhibiting Luder's strain. Hence, a more general procedure for the materials exhibiting Luder's strain is proposed. In addition, an inverse method for assessing an ‘apparent ultimate tensile stress’ (akin to the ultimate stress of ductile materials at point of zero slope) for materials with low ductility (due to quenching or carburizing) is suggested.     

Implicit yield function formulation for granular and rock-like materials

The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or ‘false elastic domains’) preventing the use of efficient return-mapping integration schemes. This problem is solved by proposing a general construction strategy to define an implicitly defined convex yield function starting from any convex yield surface. Based on this implicit definition of the yield function, a return-mapping integration scheme is implemented and tested for elastic–plastic (or -damaging) rate equations. The scheme is general and, although it introduces a numerical cost when compared to situations where the scheme is not needed, is demonstrated to perform correctly and accurately.     

Effects of approximations in analyses of beams of open thin‐walled cross‐section—part II: 3‐D non‐linear behaviour

In a companion paper, the effects of approximations in the flexural‐torsional stability analysis of beams was studied, and it was shown that a second‐order rotation matrix was sufficiently accurate for a flexural‐torsional stability analysis. However, the second‐order rotation matrix is not necessarily accurate in formulating finite element model for a 3‐D non‐linear analysis of thin‐walled beams of open cross‐section. The approximations in the second‐order rotation matrix may introduce ‘self‐straining’ due to superimposed rigid‐body motions, which may lead to physically incorrect predictions of the 3‐D non‐linear behaviour of beams. In a 3‐D non‐linear elastic–plastic analysis, numerical integration over the cross‐section is usually used to check the yield criterion and to calculate the stress increments, the stress resultants, the elastic–plastic stress–strain matrix and the tangent modulus matrix. A scheme of the arrangement of sampling points over the cross‐section that is not consistent with the strain distributions may lead to incorrect predictions of the 3‐D non‐linear elastic–plastic behaviour of beams. This paper investigates the effects of approximations on the 3‐D non‐linear analysis of beams. It is found that a finite element model for 3‐D non‐linear analysis based on the second‐order rotation matrix leads to over‐stiff predictions of the flexural‐torsional buckling and postbuckling response and to an overestimate of the maximum load‐carrying capacities of beams in some cases. To perform a correct 3‐D non‐linear analysis of beams, an accurate model of the rotations must be used. A scheme of the arrangement of sampling points over the cross‐section that is consistent with both the longitudinal normal and shear strain distributions is needed to predict the correct 3‐D non‐linear elastic–plastic behaviour of beams. Copyright © 2001 John Wiley & Sons, Ltd.     

Resistance spot weldability and high cycle fatigue behaviour of martensitic (M190) steel sheet

Resistance spot welding characteristics of martensitic sheet steel (M190) was investigated using a peel test, microhardness test, tensile shear test and fatigue test. Tensile shear test provides better spot weld quality than conventional peel test and hardness is not a good indicator of the susceptibility to interfacial fracture. Unlike DP 600 steel, the maximum load carrying capability is affected by the mode of fracture. At high load low cycle range, weld parameters have a significant difference in the S–N curves. But, almost similar fatigue behaviour of the spot welds is noted at low load high cycle range. However, when applied load was converted to stress intensity factor, the difference in fatigue behaviour between welds and even DP 780 steel diminished. Furthermore, a transition in fracture mode, that is, interfacial and plug and hole type at about 50% of yield load were observed.
[* Note: Correction made on 16 Aug 2010 after first publication online on 28 June 2010. The authors' affiliations were corrected. Under Results and Discussion, in reference to the HAZ hazardness in the ‘Micro hardness profile’ section, Figure 2 was changed to Figure 3. In reference to the welding parameters under ‘Tensile properties’ section, note that Figure 4 represents 7/200 and Figure 5 represents 5/300. In reference to the low cycles behaviour of S‐N curves in the ‘Fatigue’ section, Figure 5 was changed to Figure 6.]