Deformation and failure of ice under constant stress or constant strain-rate

Fine-grained isotropic ice was tested in uniaxial compression at ?5°C. Tests were made under: (1) constant strain rate, and (2) constant stress, with total axial strains up to about 7%. Constant rate tests for the range 10^?7 to 10^?3 s^?1 gave stress/strain curves which exhibited two distinct yield points for rates up to about 10^?4 s^?1. The “initial yield point”, at which internal cracks begin to form at a high rate, occurred at strains in the range 0.03–0.6%, the strain for initial yielding increasing with strain rate. A secondary yield point occurred at axial strains close to 1%. However, above 10^?4 s^?1 the initial yield point became dominant and the secondary yield point disappeared. At the lowest rates (10^?7–10^?6 s^?1), the secondary yield point was distinct, but the initial yield occurred at a stress level equal to, or greater than, that for secondary yield. Constant stress tests for the range 0.8–3.8 MPa gave creep curves which had a minimum strain rate at strains close to 1%. For strains less than 0.2% the resolution and data sampling were inadequate for accurate determination of strain rate as a function of time or strain, but there were fairly clear indications of another strain rate minimum in the range of 0.01%–0.1% axial strain.Direct comparison of the results for constant stress and constant strain rate suggests that the two tests give much the same information when interpreted suitably. Detailed comparisons and interpretations of the data will be given in a subsequent paper.     

Cyclic loading and fatigue in ice

Isotropic polycrystalline ice was subjected to cyclic loading in uniaxial compression at ?5°C, with stress limits 0–2 and 0–3 MPa, and frequencies in the range 0.043 to 0.5 Hz. Stress-strain records showed hysteresis loops progressing along the strain axis at non-uniform rates. The effective secant modulus, which was about half the true Young's modulus, decreased during the course of a test. The elastic strain amplitude and the energy dissipated during a loading cycle both increased with increase of time and plastic strain. Strain-time records gave mean curves which were identical in form to classical constant-stress creep curves, with a small cyclic alternation of recoverable strain about the mean curve. The inflection point of the “creep curve”, marking the transition from strain hardening to strain softening, occurred at a plastic strain of 1% (±0.1%), which is about the same as the “ductile failure strain” found in constant stress creep tests and in constant strain-rate tests on ice of the same type at the same temperature. The dissipation of strain energy up to this “failure point” was much higher for the cyclic tests than for corresponding quasi-static tests ? 100 to 600 kPa (or kN-m/m³) in comparison to about 30 kPa. The number of cycles taken to reach the “failure point” was of no direct significance, varying greatly with stress amplitude and with frequency. The results of the tests suggest that maximum resistance under compressive cyclic loading occurs at an axial plastic strain of about 1%, which is essentially the same as the failure strain for ductile yielding under constant stress and under constant strain-rate.     

The impact behaviour of paints

The split Hopkinson pressure bar has been used to study the impact behaviour of a selection of single and multi-layer paint systems in the form of films of thickness 0.04 mm. Stress-strain curves are presented for systems comprising three coatings, coating A, coating B and coating C, in compression for strain rates of the order 5×10³ s^–1. A comparison is made between the high strain-rate behaviour and that seen at quasi-static strain rates. All tests were carried out at 23 °C. The coatings studied are shown to be strain-rate sensitive, exhibiting almost a two-fold increase in flow/yield stress between the two strain-rate regimes. At low strain rates, all the coatings deformed uniformly with no sign of fracture. At high strain rates, both coating A and coating C underwent catastrophic failure which is indicative of their susceptibility to chipping. However, this was not the case with coating B which shows no signs of fracture at high strain rates for strains up to 45%. However, a combination of coating A and coating B in alternate layers led to catastrophic fracture of the resulting two-coat multi-layer system at high strain rates.     

基于Eshelby等效夹杂理论的沥青混合料有效粘弹性质分析

利用Eshelby 等效夹杂理论研究了沥青混合料的单轴压缩蠕变行为。通过时间域内的Laplace 变换将问题线性化, 得到了沥青混合料的蠕变本构关系。开展了不同温度、应力水平条件下沥青砂的单轴压缩蠕变实验, 根据数据拟合了沥青砂四参量流变模型的模型参数。在此基础上, 预测了沥青混合料在不同温度、应力水平下的蠕变曲线, 分析了温度、应力水平对沥青混合料蠕变行为的影响。结果表明:在相同的应力水平下, 沥青混合料的应变和应变率都随温度的升高而增大, 并且在沥青软化点附近发生明显突变;在相同的温度下, 沥青混合料的应变和应变率都随加载应力的增加而增大。     

The relationship between creep and strength behavior of ice at failure

This work explores the correspondence between the results of creep and strength tests performed on isotropic polycrystalline ice. A unique experimental procedure, termed a two-mode test in the present work, allows the testing of a single specimen under conditions of constant deformation rate up to failure and constant load thereafter.Using this procedure, the prevailing values of stress, strain and strain rate can be compared at the failure point under the two test modes without the influence of specimen variation. The effect of the stress path prior to failure on the creep behavior after failure can also be investigated.Tests were performed at temperatures of ?5°C and ?10°C and initial strain rates ranged from 10^?6 to 2.2 × 10^?5 s^?1. Results indicate coincidence of the failure points from creep and strength tests in stress/strain-rate/strain space. Furthermore, it appears that within the range of variables tested, the creep behavior after the mode switch at failure is independent of the stress path experienced before failure.     

Constant strain- and stress-rate compressive strength of columnar-grained ice

Unconfined compressive strength of transversely isotropic columnar-grained ice has been investigated for loads applied normal to the longitudinal axis of the columns at the high homologous temperature of 0.96 T _m (T _m is the melting temperature) under truly constant strain and stress rates. A closed-loop, servo-hydraulic test system inside a cold room was used. Both the strain- and stress-rate dependences of upper yield stress can be expressed in terms of power laws. The observed strain-rate dependence of strength was found to be numerically the same as the dependence of viscous-flow rate on stress in constant stress creep tests at the same temperature. It is shown that the strain-rate sensitivity of yield strength compares well with previous results (obtained under constant cross-head rates using a conventional machine) only if the average strain rate to yield is used as the independent variable instead of the conventional nominal strain rate. The paper also discusses the strain and time aspects of the tests. It shows interdependence among values for compressive yield strength, strain rate, failure strain and time very similar to the interdependence among the corresponding values in tensile creep failures in metals, alloys and other polycrystalline materials at high temperatures. It is emphasized that the splitting type of brittle-like premature failure depends on the stiffness of the test system and should not be considered to be a fundamental material property. The concept of failure modulus is proposed for examining the ductile to brittle transition.     

Powder compaction interpretation using the power law

The effects of strain hardening and axial strain rate, over a wide range of rates (10^–3 to 10⁵ s^–1), on the compaction properties of a variety of pharmaceutical powders have been investigated. The powders tested are: Di Pac sugar, paracetamol d.c., Avicel and lactose. These materials have been assessed using the constants derived from the power law as a criterion to describe their behaviour. All the materials tested show, with varying degrees, a non-linear increase in the yield pressure (flow stress), the constantG, the strain rate exponentm and the strain hardening exponentn as the strain rate increases. These variations are more clear in the materials known to deform plastically, such as Avicel. This is attributable to a change either from ductile to brittle behaviour or a reduction in the amount of plastic deformation due to the time-dependent nature of the plastic flow. This, however, is explained in terms of dislocation and diffusion processes involved in the plastic deformation mechanisms during the compaction process. As the speed of compaction increases the characteristics of deformation, including the value of the strain rate exponent, the shape of the creep curve and the nature of creep rate, suggest that the creep behaviour is therefore controlled by some form of diffusion process. Meanwhile, the creep characteristics of the low and medium rate tests appear to be consistent with dislocation climb and viscous glide. For the materials tested, Avicel is found to be the most strain-rate sensitive material, while paracetamol d.c. is found to be the least strain-rate sensitive material.     

The mechanical properties of ionoplast interlayer material at high strain rates

Ionoplast material has been recently introduced and extensively used as interlayer material for laminated glass to improve its post-glass breakage behavior. Due to its sound mechanical performance, the applications of laminated glass with ionoplast interlayer have been widely extended to the protection of glass structures against extreme loads such as shock and impact. The properties of this material at high strain rates are therefore needed for properly analysis and design of such structures. In this study, the mechanical properties of ionoplast material are studied experimentally through direct tensile tests over a wide strain rate range. The low-speed tests are performed using a conventional hydraulic machine at strain rates from 0.0056 s⁻¹ to 0.556 s⁻¹. The high strain-rate tests are carried out with a high-speed servo-hydraulic testing machine at strain rates from approximately 10 s⁻¹ to 2000 s⁻¹. It is found that the ionoplast material virtually exhibits elasto-plastic material properties in the strain rate range tested in this study. The testing results show that the material behavior is very strain-rate dependent. The yield strength increases with strain rate, but the material becomes more brittle with the increase in strain rate, with the ultimate strains over 400% under quasi-static loading, and decreasing to less than 200% at strain rate around 2000 s⁻¹. The testing results indicate that simply applying the static material properties in predicting the structure responses of laminated glass with ionoplast interlayer subjected to blast and impact loads will substantially overestimate the ductility of the material and lead to inaccurate predictions of structure response. The testing results obtained in the current study together with available testing data in the literature are summarized and used to formulate the dynamic stress–strain curves of ionoplast material at various strain rates, which can be used in analysis and design of structures with ionoplast material subjected to blast and impact loads.     

Viscoelasticity, viscoplasticity, and creep failure of polypropylene/clay nanocomposites

Observations are reported on polypropylene/clay nanocomposites in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. New constitutive equations are derived in viscoelasticity and viscoplasticity of nanocomposites. Adjustable parameters are found by fitting the experimental data. The stress–strain relations are applied to the analysis of creep rupture. It is demonstrated that reinforcement of polypropylene with 1 wt.% of nanoclay induces an increase in time to failure by an order of magnitude.     

Effect of a viscoelastic interphase on the creep and stress/strain behavior of fiber-reinforced polymer matrix composites

The influence of a viscoelastic interphase on the overall creep compliances and stress/strain relationships of fiber-reinforced polymer-matrix composites under a constant stress and a constant strain-rate loading are examined. The fibers are taken to be elastic but the matrix is also viscoelastic. Evaluation of the overall property is based upon the composite cylinder assemblage and the generalized self-consistent scheme. It is found that, except for the axial tensile behavior, which is fiber-dominated, the creep and stress/strain responses under transverse tension, transverse shear, axial shear, and plane-strain biaxial tension, are all significantly influenced by the interphase. A detailed examination of these effects in the light of the interphase property and volume concentration is carried out, and the results reveal that, when the interphase is viscoelastically softer than the matrix, its presence will cause a very pronounced influence on the creep strength and load-carrying capacity of the three-phase system.     

Assessment of power law creep constants of Gr91 steel using small punch creep tests

A method for determining the power law creep constants using the small punch (SP) creep test is studied. We performed elastic-plastic-secondary creep finite-element (FE) analysis of Gr91 (ASTM A387 GR91 CL2) steel using the properties at 565 °C to investigate the evolution of stress and strain rate at the weakest location of the SP creep specimen, i.e. at the annular region located at about 0.7 mm from the centre of the specimen. Empirical relations that correlate the applied load to the equivalent stress and the punch displacement rate to the equivalent creep strain rate are suggested on the basis of the finite-element stress analysis results. These simple relations enable us to achieve the constitutive relation of equivalent stress and equivalent creep strain rate under small punch creep test condition. To validate this approach, SP creep tests were conducted and creep constants were evaluated by using the proposed relations. These evaluated creep constants were then compared with those measured from standard uniaxial creep test. It is shown that creep constants evaluated from the SP creep test and the proposed method are in a good agreement with those from the uniaxial creep test.     

Nonlinear Viscoelastic,Viscoplastic Characterization of Unidirectional GF/EP Composite

Viscoplastic strains of unidirectional continuous fiber composite (HEXCEL GF/EPprepreg system) are studied experimentally and theoretically. Creep and strainrecovery tests are used. Schapery's nonlinear viscoelastic viscoplasticconstitutive equations are used and generalized to describe inelastic behavior ofunidirectional composite under isothermal creep and strain recovery conditions. Themethodology to quantify the viscoplastic strains with respect to applied stress isproposed. Viscoplastic strains of composite are described by plastic shear strain inmaterial symmetry axis. Assumptions has been used and validated that the functiondescribing the stress and time dependence of viscoplastic strain can be presented asa product of two, time and correspondingly stress dependent, master curves.     

树盘干缩异向性引起应变的测算及分析

研究探讨了干燥过程中树盘受抑制干缩应变、自由干缩应变、弹性应变、黏弹性蠕变应变以及机械吸附蠕变的图像解析测算法;运用该方法测算了白桦树盘常规缓慢干燥(含水率分布均匀)过程中干缩异向性引起的弦向各应变,分析了干燥过程中不同含水率阶段的应力状态及应力与各应变的关系。结果表明:应变的图像解析测算法可满足精度要求;树盘干燥至fiber saturation point(FSP)以下,弦向首先受拉伸应力作用,随着干燥的进行,拉伸应力转变为压缩应力;应力方向与各应变对应关系不同,与黏弹性蠕变应变无明显对应关系,与机械吸附蠕变基本对应。     

Einfluß von last- und verformungsgesteuerten mehrachsigen Beanspruchungen auf die Anrißlebensdauer

Influence of load- and deformation-controlled multiaxial tests on fatigue life to crack initiation Generally, areas of components with notches or geometrical transitions are critical because of the resulting stress/strain concentrations. In these areas due to the stress-gradients and constraint local deformations are displacement controlled even if the material's yield stress is exceeded, as long as the deformations are below the structural yield point. Therefore, load controlled tests in the elasto-plastic region with unnotched specimens from ductile materials under combined axial loading and torsion are not suitable for the interpretation of component's behaviour because of uncontrolled local deformations. Thus, the influence of multiaxial stress/strain states on the fatigue behaviour of a component under elasto-plastic deformations can be determined reliably with unnotched specimens only by deformation controlled tests, if cyclic creep is not expected in critical areas.     

Effect of hydrostatic pressure on the yield and fracture of polyethylene in torsion

Yield and fracture of polyethylene have been studied in torsion tests under superposed hydrostatic pressures. Two ductile-to-brittle transitions have been observed. At high strain rates and pressures, a conventional ductile-to-brittle transition was found with increasing strain rate and pressure. A second ductile-to-brittle transition was observed at low strain rates with decreasing strain rate. The yield stress showed a region of low, relatively constant, rate dependence at low strain rates, high temperatures and low pressures and a second region of higher strain-rate dependence at high strain rates and pressures. In contrast, the fracture stress was found throughout to have a relatively constant strain-rate dependence of intermediate value between those obtained for the yield stress. These features confirmed that failure can be considered as competition between yield and fracture processes. The fracture stress became lower than the yield stress at both high and low strain rates where brittle fracture was observed, with fully ductile behaviour resulting in intermediate conditions where the fracture stress exceeded the yield stress. The pressure, strain rate and temperature dependence of the yield stress was well described by two Eyring processes acting in parallel, both processes being pressure dependent.     

A numerical study of ductile void growth under dynamic loading conditions

A numerical study of void growth at differing global strain rates in the range 149 s^–1–2240 s^–1 and at start temperatures between 173 K and 573 K has been carried out for a material containing a three-dimensional periodic array of equally spaced, initially spherical voids. To take account of the effect of strain rate and temperature on the flow stress under dynamic adiabatic conditions, the well-established Zerilli-Armstrong constitutive relations for pure copper and iron have been employed. An instability criterion based on the maximum mean tensile stress has been used to identify the point at which unstable void growth occurs. For both materials, the strain at instability has been found to be dependent on stress triaxiality and start temperature but only weakly affected by strain-rate     

Analysis of Garofalo equation parameters for an ultrahigh carbon steel

Isothermal stress–strain curves data from torsion tests conducted at high temperature (950–1200 °C) and strain rates (2–26 s⁻¹) were analyzed in an ultrahigh carbon steel (UHCS) containing 1.3%C. The sine hyperbolic Garofalo equation was selected as an adequate constitutive equation for the entire range of the forming variables considered. The Garofalo parameters were assumed strain dependent allowing the prediction of stress–strain curves under transient and steady-state conditions. The average relative errors obtained were below 3% in stress. In addition, the creep deformation mechanisms in the UHCS were analyzed from the Garofalo equation parameters. For this aim, the stress exponent of the Garofalo equation was, for the first time, related to that of the power law equation. The results show that the controlled deformation mechanism at steady state is lattice diffusion-controlled slip creep.     

Creep failure of polypropylene: experiments and constitutive modeling

Observations are reported on isotactic polypropylene in uniaxial tensile tests with various strain rates, relaxation tests with various strains, and creep tests with various stresses at ambient temperature. Constitutive equations are derived for the viscoelastic–viscoplastic responses and damage of a semicrystalline polymer at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The model is applied to predict creep-failure diagrams in the entire interval of stresses. A phenomenological approach is proposed to determine a knee stress, at which transition occurs from ductile to brittle rupture. Accuracy of this method is evaluated by numerical simulation.     

Constant stress creep and constant true strain-rate tensile tests of the superplastic alloy PbSn

Strain-time curves and stress-strain curves have been obtained for the superplastically deformed PbSn eutectic tested in creep under constant stress and in tension under true strain-rate conditions at temperatures ranging between –44 and 30° C. It is shown that the flow stress does not depend on strain and time and is only a function of the true strain rate, of the temperature and of the initial grain size. The result is that this superplastic alloy does not strain-harden and that the grain size is constant. The apparent activation energy does not depend on stress and temperature and is equal to 11.5±0.5 kcal/mole.