FATIGUE FAILURE AT STRESSES BELOW FATIGUE LIMIT

In the present study, the authors have focused attention on the internal stress in a material. A stress applied to a specimen does not fully act to deform the material. The effective stress which actually acts on dislocations depends on the internal stress in the material. The origin of the internal stress is attributed here to the dislocation structure. From this viewpoint, fatigue tests were carried out and the following results were obtained: (1) The origins of the internal stress and the effective stress were clarified by means of a dislocation model. (2) The behaviour of the internal stress during the fatigue process showed clear differences between over-stressed and under-stressed states. (3) The concept of internal and effective stresses assists in our understanding of the fatigue phenomenon. (4) The mechanism of fatigue failure in the under-stressed fatigue state was also studied, and the concept of an internal stress was applied to instances of practical fatigue situations.     

Internal stress and unloading experiments in creep

Internal stresses are developed during deformation and have an important role in determining the mechanical properties and, in particular, the creep properties of crystalline materials. The strain transient dip test is the generally accepted method for the determination of internal stresses developed during creep. The strain transient dip test has been analysed using a number of very general creep models and it is concluded that, for glide-controlled creep, the dip test can only be interpreted if the relation between dislocation velocity and the force on the dislocation is linear. When this is the case it measures not an average internal stress but an average back stress for all the dislocations, mobile and immobile, where the back stress is the resolved component of the internal stress plus the glide component of the line tension force divided by the Burgers vector. The dip test does not allow separation of the back stress into internal stress and line tension components. For recovery models the results of the dip test cannot be simply interpreted because expressions for the creep rate do not define a unique average internal stress or back stress. However, for the recovery model in which strain occurs by athermal or jerky glide there will be a reverse yield stress, i.e. there will be a stress reduction below which there will be instantaneous reverse strain followed by reverse creep. By averaging the instability condition for all the dislocations participating in jerky glide it is shown, subject to assumptions, that the sum of the average internal stress experienced by dislocations involved in both forward and reverse creep can be obtained from the reverse yield stress. Separate values for these internal stresses cannot be obtained, however. Determination of the reverse yield stress for recovery creep is the experiment equivalent to the strain transient dip test for glide-controlled creep.Research visitor from University of Aix-Marseille 11, France.     

Dislocation configurations and internal stresses in the creep of Nimonic 91

The internal stress, σ_i, developed during the creep of Nimonic 91 was determined as a function of applied stress, σ_a, using the strain transient dip technique. Transmission electron microscope observations of thin films of crept specimens showed Orowan dislocation loops to exist aroundγ′ phase particles at low stresses with partial dislocation loops around faultedγ′ particles at high stresses. The numbers of loops per specimen volume were counted and the resulting internal stress calculated. The results indicate that a significant part of the mechanically measured internal stress can be attributed to Orowan loops aroundγ′ particles which are stabilized against climb by the superlattice fault resulting from partial penetration of theγ′ particle by the dislocation. The variation of internal stress with applied stress can be accounted for qualitatively by the variation of loop density with stress at low stresses and the initiation of relaxation processes involving partial or complete shearing ofγ′ particles by loops at high stresses. It is suggested that creep in Nimonic 91 is dependent on the magnitude of the effective (σ_a-σ_i) and that the internal stress is determined largely by the density of dislocation loops aroundγ′ particles.     

Distribution of dislocations at a mode I crack tip and their shielding effect

Distribution of dislocations at a finite mode I crack tip is formulated. Closed form solutions for the dislocation distribution function, the dislocation-free zone (DFZ), the local stress intensity factor and the crack tip stress field are obtained. The dislocation distribution has similar features to a mode III crack model. Under a given applied stress, there may exist different configurations of plastic zone and DFZ. Crack tip shielding by dislocations depends on both applied stresses and the configuration.     

A ball-indentation method to evaluate the critical stress for dislocation generation in a silicon substrate

Although silicon substrates for semiconductor devices do not contain any dislocations initially, the thin-film stresses sometimes produce dislocations during fabricating processes. Since the dislocations degrade electrical characteristics, it is important to estimate the critical stress for dislocation generation in order to maintain the integrity and reliability of the device. Therefore, we have developed a method that uses a ball-press test for evaluating the critical stress for dislocation generation. The critical stress is calculated from the critical press load for dislocation generation. We used this test method to determine the temperature dependence of the critical stress, and found that the change of the critical stress with temperature is not so large when compared with that of the reference tensile test data. This is because, since the tensile specimen contains some dislocations or initial damage, the tensile test data probably includes the influence of the movement of these dislocations. Furthermore, the effect of ion implantation was examined and this makes clear that the critical stress of implanted specimen is decreased.     

High-temperature creep of the particlehardened commercial Al-Li-Cu-Mg alloy 8090

Creep of the particle-hardened commercial Al-Li 8090 alloy has been studied at temperatures of 425 and 445 K. The measured stress sensitivity of the minimum creep rates changes abruptly at a given applied stress with stress exponents being around 4–6 at low stresses and 30–40 at high stresses. Creep activation enthalpies were determined by both temperature cycling and by comparing creep rates at two temperatures at a given applied stress, the results from both gave the same unrealistically high values. The internal stresses, _i, developed during creep were determined using the strain-transient dip test. These increased linearly with the applied stress, _a, at low stresses and were effectively constant at high stresses. The minimum creep rate was found to be a simple function of the effective stress, _a-_i, with a stress exponent of between 5 and 6, at all applied stresses. The dislocation and precipitate structure of the alloy was examined before and after creep using thin-film electron microscopy. The initial structure consisted of pancake grains with a well-developed {1 1 0}1 1 2 type texture. The grains contained well-developed sub-cells and and S precipitates. The structure developed during creep consisted of dislocation pairs, single dislocations and dislocations loops. There was evidence to suggest that slip took place on both {1 0 0} and {1 1 1} planes. The dislocation loops were most likely to have been Orowan in character and around the rodlike S precipitate, with the coherent precipitate being sheared by pairs of dislocations. The measured internal stresses result from inhomogeneity of plastic deformation. These stresses increase continuously with applied stress up to the observed macroscopic yield stress, and then become constant. The internal stresses are likely to have arisen from the Orowan loops around S and the behaviour of sub-grain boundaries. The increases in internal stress may have resulted from an increased loop density with increasing applied stress. This rate of increase is likely to slow down if S particles are sheared or fractured at high applied stresses.     

Negative creep and recovery during high-temperature creep of MgO single crystals at low stresses

High-temperature creep equipment with very high precision has been used to measure the creep of MgO single crystals above 1948 K and stresses lower than 4 MPa. A transition in exponent,n, from 3 at stresses higher than 2 MPa to almost unity at lower stress region was observed. Since in a single crystal deformation can only occur by the generation and movement of dislocations, the transition in stress exponent from high to low stress region cannot be interpreted in terms of a change from dislocation to diffusional creep processes. Decreasing the stress by a small amount during steady-state creep resulted in an incubation period of zero creep rate before creep commenced at lower stress. However, large stress reduction led to a period of negative creep during which the dislocation substructure coarsens and the subgrain cell boundaries straighten. On the basis of dislocation substructure studies, it is proposed that the kinetics of backflow are thought to be based on the local network refinement caused by the reverse movement of dislocations and that recovery is necessary before further movement of dislocation can occur. It is shown that the network theory proposed by Davis and Wilshire can satisfactorily account for all stress reduction observed during forward creep.     

Creep behaviour of a heat-resistant ferritic chromium steel in terms of stress exponents

In many publications the high-temperature deformation behaviour of materials is described by the stress sensitivity of steady-state creep rate, the creep exponent, n. In order to investigate the mechanisms of dislocation motion, it is more promising to evaluate the constant structure creep properties. This leads to the constant structure creep exponent, m, which is not influenced by the stress dependence of the substructure. Therefore, the investigation of deformation mechanisms is less difficult. Additionally, m is the basis for the calculation of the effective stress exponent, m, of dislocation velocity, which permits the investigation of the strength of interactions between alloying atoms and moving dislocations. It is shown that the creep exponent, n, is between 5 and 10 in the power-law creep region (where diffusion-controlled glide processes of dislocations cause deformation). However, it increases to about 50, if exponential creep is working (in this region the glide processes are thermally activated but diffusion is not the rate-controlling mechanism). The constant structure creep exponent, m, is relatively small and independent of stress in the power-law creep region. It increases almost linearly with the applied stress, if thermally activated glide dominates creep. The evaluation of the stress exponent, m, which can be calculated from m and the effective stresses, showed that dislocation motion is influenced by alloying atoms as long as power-law creep works. There is experimental evidence that power-law breakdown is due to a breakdown of the alloying effect, because dislocations can escape from their dragging Cottrell clouds at high applied stresses.     

Effect of the Cyclic Tensile Component of Loading on the Dislocation Structure of AMg6 Alloy

We study the effect of the cyclic component under combined tension of specimens of AMg6 alloy on the evolution of the microstructure of the material along the neck of the specimen. We discovered that cyclic loading imposed on quasistatic loading results in a significant increase in dislocation density. The cyclic component of tension initiates the appearance of additional mobile dislocations, which leads to a greater strain under the same stresses.     

Application of a modified strain transient dip test in the determination of the internal stresses of PVC under tension

A modified strain transient dip test which involves the design of a load reduction apparatus to perform rapid step unloading and extrapolating to zero extension rate has been developed to measure the internal stresses (recovery and effective stress) of PVC under uniaxial tension. This simple technique appears to be consistent with other internal stress measurement techniques. It was found that the effective stress approaches a limiting value with applied strain and an extrapolated yield point could be defined. The limiting value is a function of the strain rate during the initial load application. The general increase in applied stress (at fixed applied strain) with crosshead speed was attributed to the increase in magnitude of the effective stress. The maximum peak ratio of effective over recovery stress, at each crosshead speed, could indicate that it was the energy-dissipating part of the material that played a dominant role in the early stages of the deformation while the energy-storage part dominated the latter stages.     

Discrete dislocation simulation of nanoindentation

A methodology to describe nanoindentation by means of discrete dislocations is presented. A collocation method is used to calculate the arising contact stresses at each indentation step, which permits to realize an arbitrary shape of the indenter. Distributed dislocation sources are allowed to emit dislocations on predefined slip planes, when the critical value of the local shear stress for the emission is reached. After each indentation step, the newly emitted dislocations are brought to their equilibrium positions under the influence of the stresses induced by the contact stresses and the dislocations. As an application of our model, the plastic behavior of two materials with different densities of dislocation sources will be studied in detail.This work was financially supported by the FWF (Fonds zur Förderung der wissenschaftlichen Forschung) Project P13908-N07.     

The influence of thermal residual stresses and thermal generated dislocation on the mechanical response of particulate-reinforced metal matrix nanocomposites

Due to thermal expansion mismatch between reinforcing particles and matrix, thermal induced dislocations are generated in metal matrix nanocomposites (MMNCs) during cooling down from the processing temperature. These dislocations have been identified as an important strengthening mechanism in particulate-reinforced MMNCs. In this study, the development of thermal residual stresses and thermal induced dislocations in MMNCs are predicted using discrete dislocation simulation, assuming the whole material is under uniform temperature change. Shear deformation is applied after the composites are cooled down to room temperature and the influence of thermal residual stresses and thermal generated dislocation on the overall response of particulate-reinforced MMNCs are investigated. The results show that the thermal residual stresses are high enough to generate dislocations and the dislocation density is higher in the interfacial region than the rest of the matrix. The predicted mechanical behavior of the MMNCs matches the experimental results better when thermal residual stresses are included in the simulations.     

Breakdown of the power-law creep in a Class I Al-10 at % Zn alloy

The creep behaviour of Al-10 at% Zn at 573 K is divisible into three deformation regions; low stress region, intermediate stress region and high stress region. The creep characteristics of the low stress region and intermediate stress region are consistent with dislocation climb and viscous glide, respectively. In the high stress region, the stress exponent,n increases with stress, the activation energy is higher than those observed in the other two regions, the activation area is slightly decreasing with stress and the internal stress is almost negligible. Present analysis shows that these characteristics are consistent with the thermally-activated glide motion of dislocations as a rate controlling mechanism at high stresses.[/p]     

Stress induced precipitate microstructure in anisotropic alloys

Precipitate microstructure in the anisotropic alloys under applied strain and periodic dislocations were investigated by using phase-field simulation. The results show that the ratio of shear modulus (RSM) between precipitates and matrix influences the formation of rafting structure under the applied strain. The dislocation network can induce the nanoscale precipitate pattern, and the orientation or shape of the precipitates is dominated by the dislocation stress and internal stress together. The novel nanoscale microstructure in anisotropic alloys may be controlled by the combination of internal stress, applied strain and dislocation network.     

Nanoscale mechanisms for high-pressure mechanochemistry: a phase field study

Coupled evolution of a high-pressure phase (HPP) and dislocations, including dislocation pileups and dislocations generated due to phase transformation (PT), under compression and shear of a nanograined bicrystal, is considered as a model for high-pressure mechanochemistry. Recently developed phase field approach for the interaction between PTs and dislocations at large strains and a finite element analysis are utilized. Periodic boundary conditions for displacements are applied to the lateral surfaces. It is confirmed that the shear-induced dislocation pileups may reduce the PT pressure by an order of magnitude in comparison with hydrostatic loading, and even below phase equilibrium pressure, as it was observed in some experiments. In contrast to the formulation with boundary conditions for lateral stresses, which do not exhibit the sample size effect, periodic boundary conditions lead to some suppression of PT with decreased grain and sample sizes. The local transformation work-based phase equilibrium condition is met for most of the points of the stationary phase interfaces. The interface configurations also correspond in the most cases to the constant pressure contour but with different values for different loadings. Rarely, the same is true for the constant shear stress contours. Similar phase equilibrium conditions are satisfied for the transformation work expressed in terms of stresses averaged over the transformed grain and HPP. These conditions can be used to scale up results of the nanoscale studies to the coarse-grained microscale theory. During unloading, the PT, dislocations, and plastic shear are fully reversible. Even if one pins all the dislocations before unloading starts, still the entire HPP returns back. Thus, problem with modeling metastability of the HPPs still remains open. Obtained results are applicable for interpretation of experiments on high-pressure torsion with diamond or ceramic anvils, friction, surface processing, and probably on ball milling.     

Tertiary creep and ductile fracture in Al-Zn alloy: a consequence of structure development

The cause of failure in ductile materials has been, for many years, related to the presence of cavities. However, although large cracks or cavities have been associated with final fracture, direct observation of very small cavities throughout the neck development in pure metals or solid solution alloys has never been made. Cavity nucleation requires the existence of large local effective stresses for long enough periods of time. The different stages of necking in an Al-11 wt% Zn alloy were studied since it is known that large effective stresses are produced at sub-boundaries during the secondary stage of creep. No cavities were observed. Instead, the boundaries support large effective stresses which continue to be relaxed by dislocation emission throughout all the neck development. The subgrain size decreases from about 20 m at the onset of tertiary creep to about 0.6 m at the tip of the broken specimen at the same time as the stress continuously rises due to the large reduction in section throughout the neck. The presence of coarse slip bands from the beginning of the tertiary stage is related to strain localization as the high effective stresses lead to sub-boundary breakthrough and localized extensive dislocation activity. Fracture of the specimen occurs by shear and microcrack development following the localized softening associated with sub-boundary destruction.     

Continuous plastic cracks in ordered alloys

A discrete dislocation analysis of the continuous plastic crack is carried out for ordered alloys. The crack is assumed to nucleate and reach a size where it will emit a set of lattice dislocations in order to decrease its energy. Further growth of the crack takes place elastically until it can emit the next set of lattice dislocations. Repeated emission of lattice dislocations, with elastic crack growth in between, leads to the Griffith configuration where the energy variation with size of the crack is zero. It is shown that a crack, either tensile or shear, can be stabilized by the presence of antiphase boundary energy alone. In the absence of frictional stress or with the very low frictional stresses encountered in real materials, the lattice dislocations are generated in pairs on each slip plane. However, when the frictional stress is high, the lattice dislocations are generated as single ones, giving rise to an antiphase boundary between the crack and the lattice dislocation.     

A Griffith crack shielded by a dislocation pile-up

The dislocation free zone at the tip of a mode III shear crack is analyzed. A pile-up of screw dislocations parallel to the crack front, in anti-plane shear, in the stress field of a crack has been solved using a continuous distribution of dislocations. The crack tip remains sharp and is assumed to satisfy Griffith's fracture criteria using the local crack tip stress intensity factor. The dislocation pile-up shield the sharp crack tip from the applied stress intensity factor by simple addition of each dislocation's negative contribution to the applied stress intensity value. The analysis differs substantially from the well known BCS theory in that the local crack tip fracture criteria enters into the dislocation distributions found.     

Creep in a Cu-14at.%Al solid solution alloy at intermediate temperatures and low stresses

The helicoid spring specimen technique was applied to investigate creep of a Cu-14at.%Al solid solution alloy at homologous temperatures from 0.54 to 0.65 and stresses ranging from 0.2 to 5.0 MPa. At stresses lower than about 1 MPa, Coble-type creep was found to dominate, associated with a threshold stress apparently independent either of grain size or of temperature. At stresses above about 1 MPa, another creep mechanism obviously contributes to the measured creep rate. This mechanism operating in parallel with Coble creep is characterized by the fact that the steady state creep rate is proportional to the second power of stress and inversely proportional to the third power of grain size and is most probably grain boundary diffusion controlled. This mechanism, called the non-viscous mechanism in the present work, is similar to that considered by Gifkins and Kaibyshev et al. to result from the motion of grain boundary dislocations (grain boundary sliding) accomodated by slip of lattice dislocations in thin layers along grain boundaries, although these workers assumed the creep rate to be inversely proportional not to the cube but to the square of the grain size.