Transient thermal response near dynamically-loaded cracks during dislocation generation

Summary As a step in considering thermal effects prior to dynamic fracture or the development of fully-plastic crack edge zones, a transient 2-D study of edge dislocation generation near cracks in a fully-coupled thermoelastic solid is considered. Dynamic loading is provided either by SV-wave diffraction or tension, and no heat sources are imposed upon the solid. Despite the existence of characteristic lengths in the governing equations, exact solutions to the required mixed boundary/initial value problems are obtained in the multiple transform space, and time transforms extracted by an inversion process similar to the used in classical wave propagation. From them, the temperature changes at the dislocation edges for short times after generation are developed. These show that dislocation motion and dislocation-crack interaction produce constant temperature changes that are small. However, the results for mirror pairs separating at low speeds suggest that, as dislocation arrays form in the process of plastic zone development near the crack edge, the temperature increases could well become important.     

Thermal effects in rudimentary crack edge inelastic zone growth under stress wave loading

Summary Inelastic zone growth at the edges of a pre-stressed crack due to stress-wave loading by diffraction is considered. The Dugdale zone model is used, and the surrounding material is a weakly-coupled thermoelastic solid. The growing zone acts as a heat flux site for the solid. A transient analysis for the brief period after zone growth initiation is performed and, for generality, the crack itself is allowed to extend.Expressions for the heat flux and the inelastic zone edge temperature rise are obtained, and show dependence on several important parameters. In particular, the temperature rise is enhanced by the presence of a pre-existing zone, yet varies inversely with the zone growth rate. This rise increases rapidly upon stress wave diffraction, but levels off at values on the order of those found in stress-state analyses.     

Early effects of temperature-dependent yield stress in a transient analysis of fracture

Summary A semi-infinite crack grows due to stress wave diffraction in a thermoelastic solid. A rudimentary inelastic zone at the crack edge acts both as a heat flux site and as a crack-blunting mechanism. The first-step transient analysis treats constant crack/zone extension speeds and elastic properties. The yield stress, however, is allowed to vary with temperature.A relation involving the a priori unknown heat flux in the zone and an expression for the temperature response at the zone edge are found in the period right after fracture/zone initiation.These indicate that the applied (incident wave) stress must exceed the value necessary for zone formation predicted by a non-thermal analysis. The zone edge temperature increases rapidly at first, but then begins to level off in the same range of values noted in steady-state analyses at the time limit of the model validity. This temperature rise varies inversely with zone growth rate. A temperature-dependent yield stress definitely enhances the temperature rise, although the rise histories for this and a constant yield stress do not differ markedly in form.     

Thermoelastic analysis of a partially insulated crack in a strip under thermal impact loading using the hyperbolic heat conduction theory

In this paper, the transient temperature and thermal stresses around a partially insulated crack in a thermoelastic strip under a temperature impact are obtained using the hyperbolic heat conduction theory. Fourier and Laplace transforms are applied and the thermal and mechanical problems are reduced to solving singular integral equations. Numerical results show that the hyperbolic heat conduction parameters, the thermal conductivity of crack faces, and the geometric size of the strip have significant influence on the dynamic temperature and stress field. The results based on hyperbolic heat conduction show much higher temperature and much more dynamic thermal stress concentrations in the very early stage of impact loading comparing to the Fourier heat conduction model. It is suggested that to design materials and structures against fracture under transient thermal loading, the hyperbolic model is more appropriate than the Fourier heat conduction model.     

基于断裂力学的钢框架梁柱节点抗震性能分析

介绍了8 个足尺节点试验的结果与连接焊缝断裂破坏的现象。采用二维有限元断裂模型,研究了抗弯钢框架梁柱节点的断裂行为。以I 型裂纹尖端应力强度因子K_I和J积分为定量评价指标,分析了焊接孔形式、初始缺陷尺寸及位置、焊接垫板、角焊缝补强等设计细节对节点材料断裂韧性需求的影响。弹性分析表明,切除垫板并以角焊缝补强的措施,能最有效地降低对材料韧性的要求。弹塑性分析表明,焊接高匹配时热影响区裂纹比界面裂纹对材料韧性的要求更高,且局部塑性应变累积使材料的断裂韧性降低;解释了节点试验中断裂易发生在梁下翼缘焊缝热影响区的现象。基于断裂分析得到的节点抗弯承载力与试验中节点的极限弯矩吻合较好,该文的研究为钢框架梁柱节点的防断设计提供了参考。     

A thermal-medium crack model

In analyzing the fracture behavior of a cracked thermoelastic material, of much importance are the effects of thermal loadings on the crack growth. Under the consideration of a medium in an opening crack, a thermal-medium crack model is proposed in this paper. The heat flux at the crack surfaces is assumed to depend on the jumps of the temperature and the elastic displacement across the crack. The thermally permeable and impermeable crack models are the limiting cases of a thermal-medium one. The proposed crack model is applied to solve the problem of a Griffith crack in a transversely isotropic material under thermal and mechanical loadings. Using two introduced displacement functions and the Fourier transform technique, the thermoelastic field and the elastic T-stress are determined in explicit forms by using elementary functions. Numerical results are presented to show the effects of the thermal conductivity inside a crack and applied mechanical loadings on the heat flux at the crack faces, the jumps of temperature across the crack and mode-II stress intensity factor in graphics respectively. The obtained results reveal that the mode-II stress intensity factor for a thermal-medium crack in a thermoelastic material depends not only on applied thermal loadings but also on applied mechanical ones.     

A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF DYNAMIC DELAMINATION IN COMPOSITES

Abstract A fundamental understanding of dynamic delamination in composites is sought through the application of theoretical and experimental approaches familiar to dynamic fracture mechanics. Analysis of steady-state fracture in an infinite orthotropic strip yields a simple solution which can be used to evaluate numerical procedures and experimental results. The analogous specimen consists of a single edge notched composite strip bonded to stiff steel substrates to enforce the desired displacement boundary conditions. Delamination velocities of the order of 10 to 1000 m/s were measured using a graphite gauge technique. Quasi-static and dynamic finite element methods are applied to investigate the behavior of the specimen and to determine static initiation and dynamic delamination toughness. The experimental observations cannot be explained by linear elastic fracture theory. The absence of a unique G(?) relationship might be rationalized by a simple model relating matrix crack zone size to fiber bridging mechanisms.     

Thermomechanical aspects of dynamic crack initiation

Dynamic fracture is generally addressed as an isothermal phenomenon. When specific phenomena such as shear band formation and propagation are involved, the analyses include thermomechanical conversion of strain and/or fracture energy into heat (thermoplasticity). In this case, it has been shown that very significant temperature rises can develop which cause softening of the crack-tip material. In these works, thermoelastic temperature changes at the tip of the crack are implicitly neglected. In a recent work, we have questioned this issue and shown that for a stationary crack subjected to transient loading, adiabatic thermoelastic effects were noticeable, thus causing a large temperature drop in the elastic zone surrounding the crack-tip (Rittel, 1998). In the present work, we pursue this line of investigation by presenting additional experimental results about temperature changes ahead of a dynamically loaded crack in commercial polymethylmethacrylate. We investigate mode I and mode II loading configurations. We observe, as expected, that the temperature drops for mode I loading while it rises for the mode II case. In each case, the crack initiates during the phase where the temperature changes (drop or rise). While showing that thermoelastic aspects of fracture should certainly be taken into account, the present results indicate that thermomechanical aspects in general should not be overlooked when addressing dynamic crack initiation.     

Effect of welding thermal cycles and cold working on fracture toughness of SN490 steel under static and dynamic loading

Abstract

The static fracture toughness K _IC and dynamic fracture toughness K _Id of SN490, its pre-strained steel, and its welding heat affected zone were measured. K _IC tests were conducted according to the ASTM standard, and K _Id tests were carried out on an instrumented Charpy impacting machine. The experimental results were used to determine the effects of welding thermal cycle and cold working. It was found that both welding heat input and cold working are harmful to the fracture toughness of SN490 steel under both static and dynamic loading. The deleterious effects are serious under static loading. The detrimental effect of welding heat input during submerged arc welding was found to be more significant than that of the 10% plastic prestrain.     

Dynamic delamination growth in laminated composite structures

The dynamic growth of a thin strip delamination in a thick base laminate under in-plane loadings has been analysed. A variational principle, coupled with a Griffith-type fracture criterion, is used to formulate the delamination growth problem. Two approximate solutions, including one mode and two modes, respectively, are calculated in this paper. The resulting equations of motion and the dynamic local growth condition at the crack tip turn out to be two and three coupled ordinary differential equations for one-mode and two-mode solutions. A fourth-order Runge-Kutta method is then used to obtain the numerical solutions. The results show that delamination growth will approach a state of arrest for materials with high fracture toughness, and continue all the way without a limit for low fracture toughness materials. The inertial effect is important and should not be ignored in calculation of the arrested delamination length for high fracture toughness materials. For materials with low fracture toughness, the inertial effect is significant and high admissible modes are noticeable. A comparison between the present results and the previously known quasi-dynamic solution is also given.     

Hybrid finite element analysis of transient thermoelastic fracture problems subjected to general heat transfer conditions

This paper presents the singular characteristics of heat flux in the vicinity of the crack-tip for two dimensional transient thermoelastic fracture problems subjected to general heat transfer conditions at crack surfaces. Based on a restricted variational principle, a rigorous hybrid finite element procedure is then developed to perfectly describe the singularities of heat flux and thermal stress induced at the crack-tip. For verification purposes, the examples of transient thermoelastic problems with insulated crack surfaces are first analyzed. Excellent agreements between the computed results and referenced solutions can be drawn. To evaluate the influence of heat convection and radiation on the computation of temperature distributions and thermal stress intensity factors, several numerical examples are also presented.     

Fracture toughness of short-fibre reinforced thermoplastics

The failure process of short-fibre reinforced thermoplastics is characterized by different energy dissipation mechanisms, especially by mode II debonding along the fibre/matrix interface, sliding of debonded regions, brittle or ductile matrix fracture and pull-out. It is assumed that these failure processes are acting within a certain zone ahead of the notch tip— the dissipation zone. The modes of energy dissipation are mainly affected by the matrix fracture mode (brittle or ductile) which is mainly determined by the loading rate or temperature conditions. On the basis of an energy principle and relationships for the different energy dissipation mechanisms, we propose theoretical expressions for the static and dynamic fracture toughness and we compare these with experimental results.     

混凝土断裂过程区长度计算方法研究

该文基于粘聚裂缝概念,以起裂韧度作为裂缝起裂和扩展的准则,提出了混凝土断裂过程区长度的计算方法。以Ⅰ型裂缝为例,计算了不同初始缝长和起裂韧度情况下的断裂过程区长度值,结合以往大体积混凝土的试验数据对其进行了验证。进而分析了断裂过程区长度的影响因素,结果表明：断裂过程区长度随初始缝长的增大而逐渐增大,随起裂韧度的增大而逐渐减小。     

Dynamic deformation and fracture properties of simulated weld heat affected zone of 9Cr-1Mo steel from instrumented impact tests

Abstract

Dynamic deformation characteristics such as dynamic yield stress and dynamic strain hardening exponent along with dynamic elastic-plastic fracture toughness for the different microstructural regions of heat affected zone (HAZ) of a nuclear grade 9Cr-1Mo steel have been evaluated by instrumented Charpy tests. Isothermal heat treatment at different temperatures was used to simulate the different microstructural regions in the HAZ of this steel, namely the over tempered base metal, intercritical, fine prior austenitic grained martensitic, and coarse prior austenitic grained martensitic regions. Effects of interparticle spacing on the dynamic deformation and fracture properties have been studied. It has been observed that the dynamic yield stress and the dynamic fracture toughness follow power law relationships with the interparticle spacing whereas the strain hardening exponent follows a linear fit.     

Micromechanical interpretation of fracture toughness of particulate-filled thermoplastics

The toughness behaviour of particulate-filled thermoplastics is determined by different failure mechanisms in the plastic zone and fracture process zone in front of the macrocrack such as particle-matrix debonding, shear processes or crazing and fracture of matrix fibrils. Theoretical expressions describing the critical strain causing microcrack initiation as well as the critical crack opening and the criticalJ integral value for unstable crack initiation are derived on the basis of a micromechanical analysis. Matrix properties, particle diameter, filler content and phase adhesion are taken into account. Critical particle contents and diameters caused by matrix morphology are discussed. Model calculations are compared with experimental results from acoustic emission analysis and dynamic fracture mechanics tests on PS, PVC and HDPE filled with CaCO₃ or SiO₂ particles.     

基于断裂力学的高强度钢材梁柱节点受力性能分析

为了研究国产Q460C高强度结构钢材梁柱节点的断裂行为,该文基于断裂力学理论,计算了Q460C高强度钢材焊缝及热影响区材料的断裂韧性,并且采用三维有限元断裂模型,以I型裂纹尖端应力强度因子K_I和J积分为定量的评价指标,分析了焊缝及热影响区不同长度的裂纹对梁柱节点断裂韧性的需求。弹性分析表明,K_I沿梁翼缘宽度方向呈W形分布,最大值出现在翼缘中心,且与名义弯曲应力呈线性关系,而焊根裂纹的断裂韧性需求比热影响区裂纹更高。弹塑性分析表明,J_I最大值出现在翼缘的边缘,热影响区裂纹的断裂韧性需求比焊根裂纹更高。研究结果表明,Q460C高强度钢材梁柱节点的断裂由焊根裂纹控制,断裂承载力与梁全截面塑性承载力相近,临界转角小于0.02rad,因此建议通过改善焊接工艺或局部构造来保证节点拥有足够的转动能力。     

Effects of weld strength undermatch on fracture toughness of HAZ notched weldments in a HSLA steel

In the present work the effects of weld strength undermatch on fracture toughness of heat affected zone (HAZ) have been studied. In the investigation a high strength low alloyed steel (HSLA) with 800 MPa strength class was used, and the undermatched welded joints were made with two weld strength mismatch levels. Three-point bending test specimens with crack depth to specimen width ratio a/W ranging from 0.05 to 0.5 were extracted from the welded joints. The test results show that strength mismatching gives an obvious influence on the fracture toughness of coarse grained HAZ for the undermatched joints. The lower the weld strength mismatching, the higher the fracture toughness of the HAZ. In addition the tendency of fracture toughness change with crack depths is much the same as in previous studies on base metals or weld metals, that is, fracture toughness of the HAZ is increased with reduction of crack depths. From the measured results it shows that the macroscopically mechanical heterogeneity of the welds may have more important influence on the fracture toughness of the HAZ than the meso-heterogeneity in the reheated coarse grained HAZ. Furthermore, numerical verification indicates that the stress triaxiality at crack tip may be the essential reason for the change of fracture toughness of HAZ. It is also shown that the yield strength of HAZ determined by the limit load in the three-point bend test represents the combinative effects of HAZ and its surrounding materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

The thermoelastic behaviour of semicrystalline and of glassy poly(ether-ether-ketone)

A thermoelastic evaluation, based on simultaneous measurements of the mechanical work and of the concomitant heat of deformation by a stretching micro calorimeter, was performed on semicrystalline and glassy PEEK. The objective of this study was to utilize the sensitive technique to detect differences that would account for observed effects of micro structure on mechanical performance. A clear difference was detected beyond a 0.6% strain, where the behaviour of glassy PEEK began to exhibit inelastic features such as yielding and plastic deformation. This difference between the glassy and the semicrystalline polymers was considered the reason for the superior mechanical fatigue and fracture properties produced by the latter micro structure.     

Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach

A new approach to simulating fracture, in which toughness is partitioned between the crack tip and, optionally, a process zone, is applied to dynamic fracture processes. In this approach, classical fracture mechanics determines crack tip propagation, and cohesive laws characterize process zone response and determine crack root and process zone propagation. The approach is implemented in the Material Point Method, a particle method in which the fracture path is unconstrained by a body-fitted mesh. The approach is found suitable for modeling a range of dynamic fracture processes, from brittle fracture to fracture with crack bridging. A variety of ways of partitioning toughness are explored with the aim of distinguishing model parameters via experimental measurements, particularly R curves. While no unique relationship exists, R curves, or effective R curves, on a suite of materials would provide substantial insight into model parameters. Advantages to the approach are identified, both in versatility and in regards to practical matters associated with implementing numerical fracture algorithms. It is found to perform well in dynamic fracture scenarios.