Approximation of stress-strain curves by various functions

Stress-strain curves obtained by measurements based on four different strain-rates relating to steels St 37-3 and X 10 CrAl 18 were approximated by various functions. The mathematical procedure used herein is of advantage inasmuch as no distortion through transformation of the approximating function occurs. The transition from the area of spread of Luders lines to homogeneous deformation, which occurs in steel St 37-3, is discussed.     

Approximation of stress-strain curves by a two-parameter equation

An approximation of the stress-strain curve of carbon steels has been made using a two-parameter, physically interpretable equation. The two parameters K₁ and K₂ can be correlated to variable hardening mechanisms.     

Basic methods of plotting stress-strain curves by upsetting tests

Discussion of modifications of upsetting tests considering friction and other sources of error. Tabulated compilation of the possibilities of error and other assessment criteria.     

Hot stress-strain curves of steel determined by different kinds of deformation

For the modelling of microstructure development during hot deformation operations as well as for the prediction of deformation loads stress-strain data are required. For this purpose various laboratory deformation techniques are employed. On two steel grades (medium carbon Cr-Mo steel and austenitic Cr-Ni steel) axisymmetric and plane strain compression tests as well as torsion tests were applied with the aim of comparing equivalent stress-strain curves determined by such different deformation tests. The results showed that for the calculations of deformation loads during multi-deformation industrial operations with rather small individual deformation steps, the choice of laboratory deformation test is not a critical point. Nevertheless, conflicting results are expected by an exact interpretation of stress-strain curves concerning microstructural development by using different testing methods.     

W-40%Cu合金应力-应变曲线的测定与描述

针对粉末熔渗烧结钨铜合金(W- 40%Cu)进行了应力-应变关系曲线的试验测定,为W- 40%Cu塑性加工提供基础数据;在试验基础上,应用线性插值处理方法,对实测的应力-应变曲线进行了合理扩充,为钨铜合金塑性变形过程的数值模拟提供了全面准确的数据,并且利用Originlab和Matlab软件,对应力-应变曲线进行了二维、三维及四维的描述.     

单轴压缩条件下普通混凝土柱的峰后非线性尺寸效应

将单轴压缩条件下遭受到剪切带(峰值应力之后呈现线性应变软化行为)形式的单一剪切破坏普通混凝土试样的峰后应力-应变曲线斜率的解析解推广为非线性情形.在峰值应力之前,采用Scott模型描述非线性的本构关系.剪切带的非线性应变软化本构关系由导出的最短普通混凝土试样峰后斜率反算.利用得到的峰后本构关系,对其他较长的普通混凝土试样的应力-应变曲线进行了预测.预测的峰后应力-应变曲线依赖于试样的高度,且与实验结果吻合.估算的剪切带内部平均塑性剪切应变远大于在单轴压缩条件下测得的轴向应变的极限值.若测得的峰后应力-应变曲线被视为本构关系,则普通混凝土柱的峰后延性将被极大地低估.     

Relationship between anelastic and nonlinear viscoplastic behavior of 316 stainless steel at low homologous temperature

At low homologous temperature the plastic strain rate seems to be controlled largely by dislocation glide friction. However, since a sizeable fraction of the applied stress σ is dissipated in overcoming the strong barriers due to dislocation tangles generated by strain hardening, only a portion of the applied stress is actually expended against the frictional resistance. A recent model for this process, proposed by Hart, includes the role of dislocation pile-ups at the strong barriers. The pile-ups provide a mechanism for producing the internal back stress that reflects the barrier penetration stress. They also appear in the deformation as a stored anelastic strain component. The resultant behavior at low temperature and high stress is similar to that proposed by Gupta and Li. The same model also predicts an anelastic behavior at low stress. Measurements at both high and low stress levels on 316 Stainless Steel have now shown that the predictions of the model are quantitatively consistent at both stress levels.     

Investigation into the stress-strain curves of deformation-induced ferrite transformation in a low carbon steel

A series of tests of deformation-induced ferrite transformation ( DIFT) in a low carbon steel were carried out by the Gleeble-3500 hot simulation machine at a temperature range of Ae 3 -Ar 3 . The overall stress-strain curves during DIFT can be divided into three typical types: "double-humped","single-humped"and "transitional". The peaks exhibited in the curve are involved with deformation-induced transformation which happened in grains or at the grain boundaries. According to the stress-time curve and strain-time curve,strain capacity dramatically postponed the strain-induced transformation,which leads to the start of the transformation right ahead of the finish of deformation and the majority of the ferrite transformation process mainly happened after the deformation. Deformation-induced transformation is a metadynamic transformation process with dynamic nucleation.     

Predicting the critical conditions and stress-strain curves for dynamic recrystallization in SPHC steel

 The hot compression tests were carried out on a SPHC steel at the temperature range of 900～1150℃ and strain rate range of 0.1～10s-1, which the maximum true strain is 0.8. The activation energy of tested steel was calculated, which was 299.4 KJ /mol. The critical stresses and strains for initiation of dynamic recrystallization were determined based on changes in the work hardening rate ( ) as functions of the flow stress ( ) or strain ( ), respectively. The dependence of the peak strain ( ), the peak stress ( ), and the steady state stress ( ) were determined based on the Zener-Hollomen parameter. The mathematical models of the flow stress evolution were established in the hardening and dynamic recovery region and dynamic recrystallization region, respectively. The average error between experimental and predicted curves was around 3.26%.     

Cyclic hardening in copper described in terms of combined monotonic and cyclic stress-strain curves

Hardening of polycrystalline copper subjected to tension-compression loading cycles in the plastic region is discussed with reference to changes in flow stress determined from equations describing dislocation glide. It is suggested that hardening is as a result of the accumulation of strain on a monotonic stress-strain curve. On initial loading, the behaviour is monotonic. On stress reversal, a characteristic cyclic stress-strain curve is followed until the stress reaches a value in reverse loading corresponding to the maximum attained during the preceding half cycle. Thereafter, the monotonic path is followed until strain reversal occurs at completion of the half cycle. Repetition of the process results in cyclic hardening. Steady state cyclic behaviour is reached when a stress associated with the monotonic stress-strain curve is reached which is equal to the stress associated with the cyclic stress-strain curve corresponding to the imposed strain amplitude.     

Analysis of the stress-strain curves of a modified 9Cr-1Mo steel by the voce equation

The representation of stress-strain curves by empirical relations can give first-hand information on the deformation behavior of a material. Although the constants in these equations are simple numerals for smooth fitting of the curves, a theoretical basis using dislocation interaction has been out forth bv Berastrom.[1]     

Analysis of the low part of stress-strain curves in rat skin. Influence of age and desmotropic drugs

Stress-strain behaviour of skin strips in rats at different ages or after treatment with prednisolone or D-penicillamine has been analyzed. Special attention has been paid to the lower part of the stress-strain curves. A "hump" at an extension degree of 30% of original length was noted. When rats of different ages were compared this phenomenon was observed predominantly at an age of 2 months. Futhermore, this hump was remarkable in rats treated with prednisolone. When the stress-strain curves of rats at different ages or after treatment were averaged and normalized, the most pronounced deviations were found at an age of 2 months or after prednisolone treatment. The maximum of deviation from Hooke's law occurred at a relative extension degree of 70%. Thus, the maturation process and the influence of corticosteroid affected mostly the second part of the stress-strain curve. In order to evaluate further the stress-strain curves 3 consecutive tangents of the stress-strain curves indicating modules of elasticity were evaluated. The first and second modules of elasticity showed a minimum at an age of 2 months, whereas the ultimate elasticity modules increased with maturation up to a maximum at 12 months followed by a decrease similar to that observed in tensile strength at an age of 24 months.     

高地应力区的岩爆及其判别

为了探究更为符合工程实际的岩爆倾向性评判方法,对岩爆倾向性及其不确定性问题进行了研究. 首先,建立改进的黏结强度弱化−摩擦强度强化模型,结合能量指标实现岩爆倾向性分析;依托埋深超千米的大红山铜矿工程,将点估计−有限元分析应用于岩爆倾向性评判,构建分析模型;进一步求得岩爆倾向性的概率模型,并得到直观的概率分布情况. 结果表明：所用本构及指标可较好地进行岩爆倾向性分析,考虑参数变异性后,95%置信度的岩爆深度与现场记录深度吻合度较高,岩爆角度范围也基本吻合,比仅取定值更为准确,验证了所作不确定性分析的可行性与正确性. 不同统计指标符合不同的分布函数,岩爆深度、范围角及完全能量释放值的最优分布分别为Normal分布、Gamma分布及Lognormal分布. 基于深度及范围角指示,以80%、40%、20%为界限,可将倾向性概率划分为极大、大、中、小四个等级区间,岩爆区域的概率分布图可以更为直观合理地判断出岩爆破坏的区域和概率. 研究结果对岩爆支护及风险评估具有参考意义.     

Multigrid solution of the nonlinear Poisson-Boltzmann equation and calculation of titration curves

Although knowledge of the pKa values and charge states of individual residues is critical to understanding the role of electrostatic effects in protein structure and function, calculating these quantities is challenging because of the sensitivity of these parameters to the position and distribution of charges. Values for many different proteins which agree well with experimental results have been obtained with modified Tanford-Kirkwood theory in which the protein is modeled as a sphere (reviewed in Ref. 1); however, convergence is more difficult to achieve with finite difference methods, in which the protein is mapped onto a grid and derivatives of the potential function are calculated as differences between the values of the function at grid points (reviewed in Ref. 6). Multigrid methods, in which the size of the grid is varied from fine to coarse in several cycles, decrease computational time, increase rates of convergence, and improve agreement with experiment. Both the accuracy and computational advantage of the multigrid approach increase with grid size, because the time required to achieve a solution increases slowly with grid size. We have implemented a multigrid procedure for solving the nonlinear Poisson-Boltzmann equation, and, using lysozyme as a test case, compared calculations for several crystal forms, different refinement procedures, and different charge assignment schemes. The root mean square difference between calculated and experimental pKa values for the crystal structure which yields best agreement with experiment (1LZT) is 1.1 pH units, with the differences in calculated and experimental pK values being less than 0.6 pH units for 16 out of 21 residues. The calculated titration curves of several residues are biphasic.     

Energy dissipation efficiency in aluminum dependent on monotonic flow curves and dynamic recovery

In the hot working of Al, the flow curves are usually monotonic, reaching saturation at a lower strain ε_s and stress σ_s as temperature rises and strain rate declines. Microstructural examination confirms that the dislocation density rises to a steady-state level through formation of an equiaxed subgrain substructure with constant dimension that is larger for lower stress. The energy dis-sipation efficiency estimated by dynamic materials modeling for flow curves of the above type is the result of dynamic recovery, not of dynamic recrystallization, which is characterized by flow curves with a peak and marked softening to a steady-state regime. Formerly with Concordia University     

Time course of forward masking tuning curves in cat primary auditory cortex

Nonsimultaneous two-tone interactions were studied in the primary auditory cortex of anesthetized cats. Poststimulatory effects of pure tone bursts (masker) on the evoked activity of a fixed tone burst (probe) were investigated. The temporal interval from masker onset to probe onset (stimulus onset asynchrony), masker frequency, and intensity were parametrically varied. For all of the 53 single units and 58 multiple-unit clusters, the neural activity of the probe signal was either inhibited, facilitated, and/or delayed by a limited set of masker stimuli. The stimulus range from which forward inhibition of the probe was induced typically was centered at and had approximately the size of the neuron's excitatory receptive field. This "masking tuning curve" was usually V shaped, i.e., the frequency range of inhibiting masker stimuli increased with the masker intensity. Forward inhibition was induced at the shortest stimulus onset asynchrony between masker and probe. With longer stimulus onset asynchronies, the frequency range of inhibiting maskers gradually became smaller. Recovery from forward inhibition occurred first at the lower- and higher-frequency borders of the masking tuning curve and lasted the longest for frequencies close to the neuron's characteristic frequency. The maximal duration of forward inhibition was measured as the longest period over which reduction of probe responses was observed. It was in the range of 53-430 ms, with an average of 143 +/- 71 (SD) ms. Amount, duration and type of forward inhibition were weakly but significantly correlated with "static" neural receptive field properties like characteristic frequency, bandwidth, and latency. For the majority of neurons, the minimal inhibitory masker intensity increased when the stimulus onset asynchrony became longer. In most cases the highest masker intensities induced the longest forward inhibition. A significant number of neurons, however, exhibited longest periods of inhibition after maskers of intermediate intensity. The results show that the ability of cortical cells to respond with an excitatory activity depends on the temporal stimulus context. Neurons can follow higher repetition rates of stimulus sequences when successive stimuli differ in their spectral content. The differential sensitivity to temporal sound sequences within the receptive field of cortical cells as well as across different cells could contribute to the neural processing of temporally structured stimuli like speech and animal vocalizations.     

Time dependent crack growth in ceramic matrix composites with creeping fibers

Crack growth in ceramic matrix composites with creeping fibers has been investigated using a time dependent bridging law to describe the effect of fibers bridging a matrix crack. The fibers were assumed to creep linearly and the matrix was assumed to be elastic. Time dependent crack growth was predicted assuming that matrix crack growth occurs when the stress intensity factor at the matrix crack tip reaches a constant critical value. Crack growth rates are presented as a function of crack length and time. Domains of stable and unstable crack growth are outlined. The solutions illustrate that stable crack growth consists of a relatively brief period of decerelation followed by acceleration to large crack lengths, with crack velocity approaching constancy only at loads very near the matrix cracking stress and for very long cracks. Finally, the time needed to grow a long matrix crack is compared with a rough estimate for the time needed to rupture fibers. A transition is expected from life dominated by matrix crack growth at low stress to life dominated by fiber creep rupture after crack growth at higher stresses.