Creep in pure and two phase nickel-doped alumina

Creep in pure and two phase nickel-doped alumina has been investigated in the stress range 0.70 to 4.57 kgf mm^–2 (1000 to 6500 psi), and temperature range 1450 to 1800° C, for grain sizes from 15 to 45 m (pure alumina) and 15 to 30 um, (nickel-doped alumina). The effect of stress, grain size and temperature on the creep rate suggests that diffusion controlled grain-boundary sliding is the predominant creep mechanism at low stresses and small grain sizes. However, the stress exponents show that some non-viscous boundary sliding occurs even at the lowest stresses investigated. This mechanism is confirmed by metallographic evidence, which shows considerable boundary corrugation in the deformed aluminas. At higher stresses and larger grain sizes the localized propagation of microcracks leads to high stress exponents in the creep rate equation. The nickel dopant, which introduces an evenly distributed spinel second phase into the alumina matrix, increases the creep rate and enhances boundary sliding and localized crack propagation. The weakening effect of the second phase increases with grain size, and tertiary creep occurs at strains of 0.5% and below in large grained material.     

Creep mapping in a polycrystalline ceramic: application to magnesium oxide and magnesiowustite

The construction of deformation mechanism maps for a polycrystalline ionic solid in which anion and cation transport are coupled has been demonstrated. Because of anioncation ambipolar coupling, two regimes of Coble creep are possible in systems where anion grain boundary transport is rapid: (1) rate-controlled at low temperatures and small grain sizes by cation grain-boundary diffusion, and (2) rate-limited at high temperatures and large grain sizes by anion grain-boundary diffusion. A new type of deformation mechanism map was introduced in which the temperature and grain size were primary variables. This map was shown to be particularly useful for materials which deform primarily by diffusional creep mechanisms. Ambipolar diffusional creep theory was used to construct several deformation mechanism maps for polycrystalline MgO and magnesiowustite over wide ranges of stress, grain size, temperature and composition.     

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.     

The effect of the diffusion creep behavior on the TSV-Cu protrusion morphology during annealing

As through-silicon vias (TSVs) are key structural elements of 3D integration and packaging, creep deformation, which causes TSV-Cu protrusion, is critical for TSV reliability. Here, the effect of the diffusion creep behavior on the TSV-Cu protrusion morphology is analyzed using experiment and simulation. The protrusion morphology of TSV-Cu after annealing treatment is examined using a white light interferometer. The diffusion creep mechanism of TSV-Cu is determined by observation of the TSV-Cu microstructure using a scanning electron microscopy and a focused ion beams. The TSV-Cu grain size is measured using an electron backscatter diffraction system. The diffusion creep rate model of TSV-Cu is deduced based on the energy balance theory and is introduced into the finite element model to clarify the influence of diffusion creep on TSV-Cu protrusion. It is determined that the diffusion creep of TSV-Cu is mainly caused by grain boundary diffusion and grain boundary sliding. The diffusion creep strain rate is positively correlated with the ambient temperature and the external load but negatively correlated with the grain size. The amount of TSV-Cu protrusion increases with decreasing grain size. The simulation results show that the “donut”-shaped protrusion morphology is more likely to occur in TSV-Cu with smaller grain sizes near the sidewall region of the via.     

Constitutive models of creep for lead-free solders

The constitutive modeling of creep has been extensively studied due to the important of the creep failure mode in solder joints. However, there are very few studies that considered room temperature aging contributions in their creep modeling studies. This study investigated constitutive modeling of creep of solders by taking into account the possible contribution room temperature aging. Lead-free solder (Sn–4.0Ag–0.5Cu) was found to have a higher creep resistance than Sn–Pb solder at the same stress level and testing temperature. The higher creep resistance was contributed by the second phase intermetallic compounds, Ag₃Sn and Cu₆Sn₅. The precipitation of these intermetallic compounds can significantly block the movement of dislocations and increase the creep resistance of the material. Constitutive models of creep for both lead-free and Sn–Pb eutectic solders were constructed based on the experimental data. The activation energy for SAC405 is much higher than that of Sn–Pb, which also indicates that SAC405 possesses higher creep resistance. The constitutive models can be used in finite element analysis of actual electronic packages to predict solder joint failure. The creep mechanisms of both lead-free and Sn–Pb eutectic solders were also extensively discussed in this dissertation. Dislocation gliding and climb is believed to be the major failure mode at high stresses, while lattice diffusion and grain boundary diffusion is believed to be the major failure mode at low stress levels. Grain boundary sliding is believed to contribute to creep deformation at both high-stresses and low-stresses. For eutectic Sn–Pb, superplastic deformation is a major the creep mechanism at low-stresses and high-temperatures.     

超塑性Y-TZP的压缩塑性形变

通过恒定横梁速度和恒定载荷压缩试验,对超塑性3mol％Y₂O₃稳定四方ZrO₂多晶体的压缩塑性形变进行了研究．测定了平均晶粒尺寸从0．30～1．33μm的3Y－TZP材料的塑性流动应力,应力指数和蠕交活化能;用扫描和透射电镜观察了试样的显微结构．结果表明,3Y－TZP材料塑性形变的机理为扩散适应的晶界滑移．随着晶粒尺寸由0．30μm增大至1.33μm,应力指数从3．2减小至1．4,活化能从580kJ／mol减小至500kJ／mol．形变机理随晶粒大小发生变化．对于晶粒较粗的3Y－TZP材料,当应变速率较高时,形变过程中在材料内产生晶间孔穴．     

Cyclic Creep Deformation and Fracture of a Cr-Mo Rotor Steel at Elevated Temperatures

Static creep and cyclic creep tests were carriedout on a Cr-Mo rotor steel from 0.5 to 0.6 T_m.Cyclic creep retardation occurred under the testconditions.With an increase of stress frequency,cyclic creep strain rate decreases and rupture timeincreases.The cyclic creep strain rate for the stresswave of a square shape is higher than that of a tri-angle shape.The apparent stress exponent of cycliccreep and the apparent activation energy of cycliccreep are both higher than those of static creep.Theminimum strain rate is inversely proportional torupture time for both static and cyclic creeps at dif-ferent stresses,temperatures,frequencies and waveshapes.The cyclic creep retardation mechanism wasexplored by the observation and analysis of the dis-location structure and fracture surface.     

Superplasticity

Superplasticity is the phenomenon of extraordinary ductility exhibited by some alloys with extremely fine grain size, when deformed at elevated temperatures and in certain ranges of strain rate. To put the phenomenology on a proper basis, careful mechanical tests are necessary. These are divided into (i) primary creep tests, (ii) steady state deformation tests, and (iii) instability and fracture tests, all of which lead to identification of macroscopic parameters. At the same time, microstructural observations establish those characteristics that are pre-requisites for superplastic behaviour. Among the macroscopic characteristics to be explained by any theory is a proper form of the equation for the strain rate as a function of stress, grain size and temperature. It is commonly observed that the relationship between stress and strain rate at any temperature is a continuous one that has three distinct regions. The second region covers superplastic behaviour, and therefore receives maximum attention. Any satisfactory theory must also arrive at the dependence of the superplastic behaviour on the various microstructural characteristics. Theories presented so far for microstructural characteristics may be divided into two classes: (i) those that attempt to describe the macroscopic behaviour, and (ii) those that give atomic mechanisms for the processes leading to observable parameters. The former sometimes incorporate micromechanisms. The latter are broadly divided into those making use of dislocation creep, diffusional flow, grain boundary deformation and multimechanisms. The theories agree on the correct values of several parameters, but in matters that are of vital importance such as interphase grain boundary sliding or dislocation activity, there is violent disagreement. The various models are outlined bringing out their merits and faults. Work that must be done in the future is indicated.     

基于EBSD技术的P91钢蠕变过程中小角度晶界演化行为表征

在620℃、145 MPa条件下对给定的P91钢进行高温蠕变持久与间断试验,采用电子背散射衍射(EBSD)技术研究其在蠕变过程中小角度晶界的演化行为。通过引入EBSD图像中的取向差分布来表征小角度晶界处(0.5~5°)的边界位错密度,分析了边界位错密度在蠕变过程中与小角度边界的数量、塑性应变以及内部微观组织演化之间的关系。此外,通过改变EBSD像素点与像素点之间的计算步长,探讨了步长选择对边界位错密度计算结果的影响。结果表明,小角度晶界处的位错密度在蠕变过程中先迅速上升,在最小蠕变率处达到极值后缓慢下降,直到最后基本保持不变;同时,EBSD的计算步长越小,得到的位错密度值越准确。     

超塑性本构模型材料参数识别方法研究

金泉林等提出的超塑性本构关系考虑了三种微观变形机制和晶粒生长过程,但单纯依靠实验很难准确的测定该本构关系的材料参数。应用遗传算法和Levenberg-Marquardt算法,以Ti-6Al-4V为例,识别该超塑性本构关系中的材料参数。计算结果和实验结果符合的很好。最后讨论了各种微观变形机制的体积分数与应变、应变率和晶粒尺寸之间的关系,发现在大部分情况下扩散蠕变机制对超塑变形的贡献可以忽略。     

Discontinuous precipitation of M23C6 in austenitic steels

Grain boundary precipitation of M₂₃C₆ has been studied in a 20% Cr-35% Ni stainless steel with two grain sizes during creep deformation at 700°C as well as during an ordinary ageing treatment at 700°C. A special etching technique was applied which showed how the grain boundary precipitation gave rise to depletion of alloying elements in a zone of uniform thickness, independent of the carbide distribution, and with a gradual decrease of the depletion towards the grain interior. At some places the carbide precipitation and grain boundary migration co-operated and in these cases there was a sharp change in alloying content across the grain boundary. This process was more frequent in creep tested samples and the degree of co-operation was larger in the coarse-grained material where even a few cases of lamellar, eutectic-like precipitation was observed. Such a grain size dependence is expected theoretically and is caused by the large difference in diffusivity between carbon and the other alloying elements. It is proposed that the various degrees of co-operation between carbide precipitation and grain boundary migration are all examples of discontinuous precipitation. The various proposed mechanisms for grain boundary migration during discontinuous precipitation are discussed on the basis of the present results.     

Influence of grain size on the mechanical behaviour of some high strength materials

Combining in an additive or synergetic manner the most potent strengthening mechanisms available in an alloy is the art of the metallurgist. The various models proposed in the literature in order to interpret the Hall-Petch relation are critically reviewed by comparison with experimental data. The pile-up models and the work hardening theories must include the inner structure of the grain in the case of alloys hardened by a second phase. Similarly, the properties and structure of the grain boundaries are influenced by impurities or the presence of particles. Ultra-fine grain sizes can provide ductility to high strength materials when surface preparation eliminates microcracks.In steady-state creep equations, introducing the influence of grain size in complex alloys by incorporating the Hall-Petch stress as one component of the internal stress helps in rationalizing the existence of an optimal grain size where creep resistance is maximized. Slower crack growth rates can be obtained by controlling the grain boundary structure as well as grain size. Fatigue tests at room temperature clearly point out the interest of small grain sizes for reducing crack initiation, usually associated, however, with lower propagation threshold and somewhat faster growth rates.     

A theoretical upper limit to Coble creep strain resulting from concurrent grain growth

The rate of diffusional creep varies with grain size x, either as 1/x ² or 1/x ³, depending on whether lattice or grain boundary diffusion is dominating. Since the rate of grain growth is proportional to 1/x ^p, where p1, the creep and grain growth relationships can be combined to predict the transient creep that results from the two processes operating concurrently. An important result is obtained for grain boundary diffusion creep (Coble creep), where two regimes of behaviour are predicted depending on the value of p. For normal grain growth (p=1) and up to a critical value p=2, the transient gives rise to an upper limit to the grain boundary diffusional creep strain. For p>2, no limiting strain is predicted. The role of the limiting strain is discussed in the context of the various experimental attempts that have been made to verify the Coble mechanism.     

Superplastic power-law creep of Sn–40%Pb–2.5%Sb peritectic alloy

The power law-creep behavior of superplastic Sn–40Pb–2.5Sb alloys with different grain sizes has been investigated at room temperature. Stress exponent values for these alloys have been determined by indentation creep, conventional creep and uniaxial tension tests in order to evaluate the correspondence of indentation creep results with conventional tests. In all cases, the indentation results were in good agreement with each other and with those of the tensile and conventional creep tests. The average stress exponent values of about 2.6 and 3.0 corresponding to the strain rate sensitivity (SRS) indices of 0.33–0.39, depending on the grain size of the materials, indicate that the grain boundary sliding is the possible mechanism during creep deformation of Sn–Pb–Sb alloys. Within limits, the indentation tests are thus considered useful to acquire information on the creep behavior of small specimens of these soft tin–lead–antimony alloys at room temperature. It is also demonstrated that the indentation creep test provides a convenient method to measure SRS and thereby to assess the ability of a material to undergo superplastic deformation.     

Deforming Nanocrystalline Metals: New Insights,New Puzzles

Recent experiments have brought new insights into the mechanisms which govern the plasticity of nanocrystalline metals. In particular, new opportunities have arisen from the finding that bulk nanocrystalline samples with extremely small grain size, prepared by the inert gas condensation technique, can be deformed to large true strain. The findings elucidate the roles of creep, partial dislocation activity along with its consequences, faulting and twinning, as well as grain boundary sliding and grain rotation. However, they also rise intriguing new questions, specifically with respect to the mechanisms of dislocation nucleation at grain boundaries, and with respect to slip system selection and alignment in twinned grains. An emerging insight is that there is not ‘the’ deformation mechanism at small grain size; instead, deformation mechanism maps in, for instance, the parameter space spanned by the strain rate and the grain size, are more appropriate representations of the various processes that control the materials behavior.     

Localized plastic flow autowaves and the Hall-Petch relation in aluminum

Characteristics of the plastic strain macrolocalization are compared to parameters of the Hall-Petch relation for the flow stress in polycrystalline aluminum samples with grain sizes ranging from 0.008 to 5 mm. It is established that, in the range of brain sizes studied, there are two possible types of the dependence of the length of localized strain autowave on the grain size and two variants of the Hall-Petch relation. It is shown that the boundary between the two variants in both cases corresponds to d ≈ 0.1 mm. Interconnection of the patterns of plastic flow localization and the Hall-Petch relation is traced.     

The activation areas for grain boundary sliding

The activation areas for grain boundary sliding in Al, Pb, Sn, Zn, and Cu are compared with those for creep in the same materials. It is found that the activation area-stress relation for grain boundary sliding is similar to that for creep. This observation is consistent with a dislocation or ledge mechanism of grain boundary sliding.     

Deformation mechanisms in an austenitic stainless steel (25Cr-20Ni) at elevated temperature

The creep behaviour at elevated temperature of an austenitic stainless steel (25Cr-20Ni), both with and without antimony additions, has been reanalysed. Formerly, the creep behaviour was interpreted by considering creep mechanisms based on diffusional (Coble) creep and threshold stresses. In the present paper, it is proposed that an alternative mechanism of grain boundary sliding, accommodated by slip in grain boundary mantle regions, can in fact be used to describe more accurately the creep behaviour. Quantitative predictions, based on phenomenological equations for describing creep controlled by grain boundary sliding, are made of the influences of grain size, stress and antimony addition on creep rates, and of the influence of grain size on the activation energy for creep of 25Cr-20Ni stainless steel. Comparison of these predictions with those based on creep models incorporating only diffusional flow are made. Furthermore, the existence of a threshold stress in creep of single-phase, massive materials is strongly questioned.     

Analysis of creep rupture in a notched tensile bar

For circumferentially notched, round tensile bars the creep rupture behaviour is analysed, based on constitutive relations that account for the nucleation and growth of grain boundary cavities in polycrystalline metals at high temperatures. Both diffusive cavity growth and growth by dislocation creep of the surrounding grains is incorporated in the model, and in some cases free grain boundary sliding is assumed. Failure by cavity coalescence is predicted at small overall strains in the range where cavity growth is constrained by the rate of dislocation creep of the grains, whereas outside this range large occur prior to failure.In the analyses for notched specimens, where the stress fields are strongly non-uniform, first failure occurs at the notch tip, and subsequently a macroscopic crack grows into the material. Various combinations of material parameters are considered, and in most cases the crack is found to grow in the plane of the notch. The results are related to earlier experimental and computational investigations of creep rupture in notched bars.     

Deformation mechanism maps for micro-grained, ultrafine-grained, and nano-grained materials

There are several deformation mechanisms that depend on grain size and are controlled by grain boundary diffusion. These mechanisms include: Coble creep, superplastic flow (micrograin superplastic flow and high-strain rate superplastic flow), and nanograin deformation. By combining the rate-controlling equations of these mechanisms and by making assumptions regarding triple-junction creep, a deformation map based on grain size was constructed. It is demonstrated that this map can account for the locations of experimental data representing three types of deformation behavior: micrograin superplasticity, high-strain rate superplasticity, and nanograin deformation.