On a thermo-mechanical effect and criterion of crack propagation

A thermo-mechanical effect from partial conversion of fracture work into heat energy during crack propagation is considered with a simple mathematical model. It is assumed that the heat production zone in the vicinity of the crack tip is very small. Thus, the crack propagation process can be viewed as propagation of the crack in elastic material with a point thermal heat source fixed at the tip of the crack. This thermal heat source generates its own temperature and stress fields around the crack tip. As shown in this paper it also generates a negative stress intensity factor that specifies fracture mode I and has to be accounted for in the energetic fracture criterion. The model developed may help to explain many experimental observations such as the increase in the specific surface energy that accompanies an increase in the crack speed and why fracture mode I has a special role in crack propagation phenomena.     

Analysis of the optical method of caustics for dynamic crack propagation

In the interpretation of experimental data on dynamic crack propagation in solids obtained by means of the optical method of caustics, it has been customary to neglect the effect of material inertia on the stress distribution in the vicinity of the crack tip. In this paper, the elastodynamic crack tip stress field is used to establish the exact equations of the caustic envelope formed by the reflection of light rays from the surface of a planar solid near the tip of a propagating crack. These equations involve the instantaneous crack tip speed, the material parameters and the instantaneous dynamic stress intensity factor, and they can be used to determine the stress intensity factor for given material parameters and crack tip speed. The influence of inertial effects on stress intensity factor measurements for system parameters typical of experiments with PMMA specimens is considered. It is found that the stress intensity factor values inferred through a dynamic analysis may differ by as much as 30–40% from values based on a quasi-static analysis.     

Thermal stresses and fracture of thin plates during cutting and welding operations

In many technological processes involving cutting or welding of thin plates there is local thermal heating or cooling at the tip of the cut by a thermal source. In this paper we analytically investigate the stress distribution induced by the point thermal source moving with a constant velocity across an infinite elastic plate. Stress intensity factor for the cut formed by the moving thermal source is calculated. It is shown that for welding the value of the stress intensity factor due to thermal stresses induced by the thermal source is equal to zero. For cutting in the case of positive values of the power of thermal source the stress intensity factors will be negative. This means that the thermal field induced by the point thermal heat source will tend to close the cut in the vicinity of the tip. The opposite situation occurs when the cut tip is cooled by the thermal source. As an example, the theory under development is shown when applied to some strength issues of thermal beam cutting of brittle materials.     

含界面裂纹圆形夹杂的十二次对称二维准晶热应力分析

针对点热源作用下,无限大十二次对称二维准晶基体和圆形弹性夹杂界面之间含多条裂纹的问题进行了研究。基于复变函数分区全纯理论、留数定理、广义 Liouville 定理、Riemann-Schwarz 解析延拓定理及复应力函数奇性主部分析方法,获得了集中热源作用于准晶基体内任意一点时,准晶基体和圆形弹性夹杂内外温度场、声子场热应力的一般复势解。由此获得了含一条界面裂纹和两条界面裂纹时温度场以及声子场热应力的封闭形式解答,将所得结果与已有结果进行了对比,验证了该方法的有效性。最后通过数值算例分析了夹杂半径、点热源强度及裂纹角度对热应力和裂纹尖端热应力强度因子的影响规律。结果表明：随着热源强度的增大,裂纹尖端的声子场热应力也逐渐增大;随着裂纹角度的增大,裂纹尖端的声子场热应力强度因子变大;随着半径的增大,热应力强度因子的变化趋势越来越明显,并且取得的峰值越高,即裂纹角度和夹杂半径的增加,促进了裂纹的扩展。这些结论为准晶材料的结构设计和使用提供了科学依据。     

Thermal effect of plastic dissipation at the crack tip on the stress intensity factor under cyclic loading

Plastic dissipation at the crack tip under cyclic loading is responsible for the creation of an heterogeneous temperature field around the crack tip. A thermomechanical model is proposed in this paper for the theoretical problem of an infinite plate with a semi-infinite through crack under mode I cyclic loading both in plane stress or in plane strain condition. It is assumed that the heat source is located in the reverse cyclic plastic zone. The proposed analytical solution of the thermo-mechanical problem shows that the crack tip is under compression due to thermal stresses coming from the heterogeneous stress field around the crack tip. The effect of this stress field on the stress intensity factor (its maximum and its range) is calculated analytically for the infinite plate and by finite element analysis. The heat flux within the reverse cyclic plastic zone is the key parameter to quantify the effect of dissipation at the crack tip on the stress intensity factor.     

Electric Current-Induced Stresses at the Crack Tip in Conductors

The electromagnetic and thermal effects on the stress distribution around the crack tip in conducting materials due to electric current are investigated. Emphases are placed on quantifying the crack growth behavior affected by the interplay between these effects. A two-dimensional finite element analysis is conducted to examine the coupled problems. The results show that the compressive stress state around the crack tip plays a decisive role in preventing the crack from further growth. The resulting normal stress in front of the crack tip caused by the Joule heat generation tends to suppress the crack growth, while the stress induced by the electromagnetic forces provides a tensile normal stress with smaller magnitude in the vicinity of the crack tip, hence promotes the crack growth. Favorable agreements between numerical analysis results and existing experimental results are achieved. By utilizing these phenomena, the electric current may be used to actively control the damage propagation, hence catastrophic failure can be prevented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Temperature fields near a running crack tip

Near a running crack tip, the plastic work rate is high. According to the theory of irreversible thermodynamics, the plastic work will be almost completely converted into heat which may lead to high temperature rise at the running crack tip. The plastic zone is regarded as the zone of the heat source, and the plastic work rate as the strength of the heat source. In this paper, the plastic work rate is derived from the solution of stress and strain fields obtained by Chitaley and McClintock[1] for a steady state crack growth under anti-plane shear in an elastic perfectly-plastic material. The dependence of the thermal conductivity on temperature has been considered and a non-linear model for temperature fields has been proposed. The numerical results for glass have been given and compared with other papers.     

Displacement Fields Around a Crack Tip in Polymers

Moiré interferometry was utilized to experimentally determine displacement fields around a crack tip in single-edge-cracked tensile PMMA and PA6/PPE/SBS alloy specimens. Vertical displacement v was expressed as functions of distance r and angle θ from the crack tip, and compared with the approximate solution of linear elastic fracture mechanics to study its applicability to polymers. The results showed that the solution agreed with the experiments in the vicinity of a crack tip in the PMMA specimens, but it yielded a discrepancy as r increased. For the alloy specimens, however, the solution gave much smaller values than the experiments. The principle of superposition was employed to determine the values of v^*(=v-v′), i.e. the difference between two displacements v and v′ which was related to a uniform strain field without a crack. The expressions for v^* and v were also introduced to analyze the effects of r, θ and load P applied to the specimen. v^* was found to be an important factor in increasing the displacements near the crack tip, and the v expression well represented the experimental results for both the PMMA and alloy specimens. This revised version was published online in August 2006 with corrections to the Cover Date.     

Crack onset at a v-notch. Influence of the notch tip radius

A criterion to predict crack onset at a sharp notch in homogeneous brittle materials has been presented in a previous paper of one of the authors. It is reviewed and improved herein. It fulfils both the energy and the strength criteria and takes an Irwin-like form involving the generalized intensity factor of the singularity governing the elastic behaviour in the vicinity of a notch tip. The prediction agrees fairly well with the experiments although it slightly underestimates the experimental measures. A cause of this discrepancy can be that a small notch tip radius blunts the sharp corner. It is analysed in this paper by means of matched asymptotics involving 2 small parameters: a micro-crack increment length and the notch tip radius. A correction is brought to the initial prediction and a better agreement is obtained with experiments on PMMA notched specimens. Experiments performed on a stiffer material (Alumina/Zirconia) show that it is less sensitive to small notch tip radii. A remaining small discrepancy between experiments and predictions can be due to some non linear behaviour of the materials near the notch tip. In addition, without new developments, the method allows to determine the stress intensity factor at the tip of a short crack emanating from a sharp or a rounded v-notch.     

Analysis of temperature distribution near the crack tip under constant amplitude loading

An analytical/numerical method has been developed to find the temperature rise near the crack tip under fatigue loading. The cyclic plastic zone ahead of the crack tip is assumed to be the shape of the source of heat generation and some fraction of plastic work done in cyclic plastic zone as heat generation. Plastic work during fatigue load was found by obtaining stress and strain distribution within the plastic zone by Hutchinson, Rice and Rosengren (HRR) crack tip singularity fields applied to small scale yielding on the cyclic stress strain curve. A two‐dimensional conduction heat transfer equation, in moving co‐ordinates, was used to obtain temperature distribution around the crack tip. Temperature rise was found to be a function of frequency of loading, applied stress intensity factor and thermal properties of the material. A power–law relation was found between the rise in temperature at a fixed point near the crack tip and range of stress intensity factor.     

含倾斜裂纹三点弯动态断裂试验研究

为研究冲击荷载下巷道围岩不同角度径向裂纹的破坏机制,采用落锤冲击加载平台和数字激光动态焦散线实验系统,以有机玻璃为试验材料,设计冲击荷载下半圆孔上不同角度裂纹的三点弯动态断裂试验,记录预制裂纹的角度α的改变对裂纹动态力学行为的影响,通过分析动态应力强度因子和裂纹扩展轨迹的分形维数对实验现象进行归纳总结。研究发现:①预制裂纹角度对裂纹尖端应变能的积累和释放的快慢有较大影响,随着角度的增大,起裂时间变短,起裂更容易,裂纹尖端应变能积累的更快;②裂纹尖端应变能释放的快慢在α=45°两侧表现出不同的规律;③不同角度裂纹的Ⅰ型动态应力强度因子随时间的变化规律具有相似性,但最大值却具有差异性;④不同角度裂纹的扩展轨迹满足一定的分形规律。     

On the dependence of the dynamic crack tip temperature fields in metals upon crack tip velocity and material parameters

Although various approximations have been used to analytically predict the temperature rise at a dynamic crack tip and its relation to the crack tip velocity or the material properties, few experimental investigations of these effects exist. Here, the method of using a high speed infrared detector array to measure the temperature distribution at the tip of a dynamically propagating crack tip is outlined, and the results from a number of experiments on different metal alloys are reviewed. First the effect of crack tip velocity in 4340 steel is investigated, and it is seen that the maximum temperature increases with increasing velocity, the maximum plastic work rate density increases with velocity and the active plastic zone size decreases with increasing velocity. Also, it is observed that a significant change in the geometry of the temperature distribution occurs at higher velocities in steel due to the opening of the crack faces behind the crack tip. Next, the effect of thermal properties is examined, and it is seen that, due to adiabatic conditions at the crack tip, changes in thermal conductivity do not significantly affect the temperature field. Changes in density and heat capacity (as well as material dynamic fracture toughness) are more likely to produce significant differences in temperature than changes in thermal conductivity. Finally, the effect of heat upon the crack tip deformation is reviewed, and it is seen that the generation of heat at the crack tip in steel leads to the localization of deformation in the shear lip. The shear lip is actualy an adiabatic shear band formed at 45° to the surface of the specimen. In titanium, no conclusive evidence of shear localization in the shear lip is seen.     

Application of the crack-bridging model for fracture resistance (R-curve behaviour) to PMMA

The rising fracture toughness behaviour of PMMA was characterized using a crack-bridging model originally developed for coarse-grained alumina that predicts a mechanism for crack resistance from the bridging of unbroken grains behind the crack tip. Based on the published experimental observation of PMMA, the craze zone behind the crack tip was thought to be analogous to the effective grain-bridging zone in the model in which the fibrils in the craze zone were related to the restraining interfacial ligaments. Self-consistent results in terms of the model were obtained which indicates that the crack-bridging model can be used to account for the fibril-toughening mechanism in PMMA.     

Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.     

The effects of hyperbolic heat conduction around a dynamically propagating crack tip

Using infrared detectors, Zehnder and Rosakis (1991, J. Mech. Phys. Solids 39(3), 385), Zehnder and Kallivayalil (1991, SPIE ISS4A, 48) and Mason and Rosakis (1992, SN Report 92-2), have recorded the temperature field around a dynamically propagating crack tip travelling at constant velocity in several metals. At the same time, Tzou (1990a, J. Heat Transfer 112, 21, 1990b, Inst. Heat Mass Transfer 33(5), 877) has suggested that the temperature field around a propagating crack tip might exhibit some of the characteristics of hyperbolic heat conduction. In this paper a corrected solution of the hyperbolic heat conduction equation for a travelling point source is derived. Then an experimental estimate of the active plastic zone (heat generating zone) at a crack tip is used for various experimental conditions to examine the possible effects of hyperbolic heat conduction around a propagating crack tip. Finally, using the actual experimental conditions of Zehnder and Rosakis (1991) Zehnder and Kallivayalil (1991) and Mason and Rosakis (1992) it is shown that no effects of hyperbolic heat conduction are observed around a propagating crack tip. It is seen that, due to adiabatic conditions at the crack tip during these experiments, the solution of the hyperbolic heat equation is indistinguishable from the solution of the parabolic heat conduction equation for crack propagation in steel.     

Technique for producing crack arrest by electromagnetic heating

Abstract

Crack arrest in current conducting materials by electromagnetic heating can be used effectively to extend the service life and improve the safety and reliability of structures and components. Theoretical analysis and experimental investigations have shown that due to heat concentration around the crack tip, small welded joints are formed by metal melting. Thus, the formation of the main crack source is prevented. From metallography, it has been found that a typical fine phase transformation microstructure can be obtained in the crack tip region as a result of rapid heating and cooling. The intensity, ductility, and wear capacity are promoted under the combined influence of superfine structure, thermal compressive stresses, and phase transformation compressive stresses. Microcracking and subsequent main crack propagation can both be prevented. The basic principles of the electromagnetic heating effect and the results of experimental work based on the theory are presented.     

Constraint issues in cleavage fracture and matters arising from practical application

In the past 10 years much research has been carried out to deal with the question of how crack‐tip constraint effects can be described and, moreover, how crack‐tip constraint (stress tri‐axiality in the vicinity of the crack tip) contributes to matters arising from practical application of structures and components containing postulated or real cracks and made of ferritic steel. In fracture mechanics, application crack‐tip constraint can be influenced by loading (out of plane or multi‐axial loading) or by the crack shape and crack depth to ligament ratio. Temperature loading of a crack in a structure is different compared to the loading condition of a fracture toughness specimen and a deep crack behaves differently compared to a short crack. In this paper a model for the prediction of cleavage fracture of ferritic steel is briefly described and summarized and the issues for practical application are pointed out. It turns out that crack‐tip constraint, induced either by loading or geometry, can be described quantitatively by local approach models, but there is still a need to understand the micro structural features behind.     

Crack Path Predictions for Temperature Sensitive Materials

The propagation of a crack into a material whose mechanical and thermal properties depend on the temperature field developed around the running crack tip is studied in the present work. This is achieved by employing the Non Steady Heat Source model, for the calculation of the temperature field surrounding the crack tip region, the dynamic version of the T-criterion of failure and the experimental data concerning the variation of thermal and mechanical properties of the material with temperature. It is proved that in the immediate vicinity of the crack tip the material properties show steep gradient. Thus, if a failure criterion is to be applied for the prediction of the path of an already traveling crack, then the current values of the mechanical properties should be taken into account. Otherwise, fallacious conclusions may be drawn. The results obtained are in satisfactory agreement with the limited experimental evidence available from literature concerning both the intensity of the temperature field developed and, also, the direction of the crack propagation. This revised version was published online in July 2006 with corrections to the Cover Date.     

The brittle-ductile transition in silicon: The influence of pre-existing dislocation arrangements

It has been shown that the value of the brittle-ductile transition temperature in specimens of silicon containing pre-cracks at the surface is strongly dependent on the pre-existing dislocation arrangement close to the crack tip. In particular, removing dislocations from the vicinity of the crack tip has the effect of raising the transition temperature, while introducing more surface dislocations by grinding reduces the transition temperature. In both cases the transition temperature remains sharp, implying that the crack tip sources have to be nucleated in the test before effective shielding occurs. The differences in the transition temperatures reflect the differences in the distances of the dislocations from the crack tips, and in the source lengths of the pre-existing sources which send dislocations to the crack tip.Specimens which are pre-stressed at the brittle-ductile transition to a K value at which crack tip sources are expected to be nucleated exhibit a gradual “soft” transition over a wide range of temperature. This result is in agreement with the predictions of the computer modelling of dislocation emission from crack tips, developed by Hirsch et.al [3,7], and together with the results on the dependence of T_c on dislocation arrangements, provides strong support for their theory of the brittle-ductile transition.     

The range of applicability of the small-scale yielding approach in theoretical investigations of yield and fracture at a crack tip

Theoretical analysis of the processes of plastic deformation and fracture in the vicinity of a sharp crack tip becomes easier if plasticity is confined to the immediate vicinity of the crack tip, for linear elastic stress intensity factors can be used to give the surrounding elastic field, and it is possible to employ a boundary layer formulation to determine the elastic-plastic field in the immediate vicinity of the crack tip. Consideration is given to the range of applicability of the small-scale yielding approach using a simple model in which slip is confined to the crack plane. A range of stress-displacement laws is considered, the object being to assess the effect of a material's flow characteristics on the range of applicability. The conclusions are discussed with respect to plane strain crack propagation in mild steel.