Statistical Analysis of Bending Strengths for Brittle Solids: A Multiaxial Fracture Problem

A general approach for the statistical analysis of brittle fracture under tensile multiaxial stress states was evaluated for a fracture criterion based on recent concepts of noncoplanar crack extension. The resultant failure expressions were applied to bend tests and used to interpret experimental results obtained with porcelain cylinders. Implications for the interpretation of bending tests and some important trends in the failiire strength with specimen size are discussed.     

Tetragonal-to-monoclinic phase transformation in CeO2-stabilized zirconia under multiaxial loading

Critical stresses for the initiation of the tetragonal-to-monoclinic phase transformation in 9Ce-TZP zirconia materials with five different grain sizes have been studied. The influence of the grain size on the critical transformation stresses has been investigated in multiaxial stress states, namely, in four-point bending, biaxial bending and torsion. It was found that phase transformation occurs as a homogeneous phase transformation with a transformation strain increasing continuously with increasing applied stress and also as an autocatalytic phase transformation with the autocatalytic formation of transformation bands normal to the maximum principal stress. An investigation of the critical transformation stresses under different multiaxial loads in the tensile regime, i.e. with positive hydrostatic stress, showed that both the homogeneous and the autocatalytic transformation do not follow the shear-dilatant criterion investigated in multiaxial compressive testing. The experiments showed that under multiaxial loading the onset of both transformation types can be predicted with the maximum principal stress transformation criterion, with the difference between the critical stresses of both transformation mechanisms strongly decreasing with grain size.     

Experimental and numerical investigation of the dynamic response of a ZrB2-SiC ceramic under uniaxial compression

The dynamic experimental tests were performed on cylindrical zirconium diboride-silicon carbide ceramic specimens under the uniaxial compression from 519 to 2861 s⁻¹. The effect of the strain rate on the dynamic response of a ZrB₂-SiC ceramic was investigated using experimental and numerical methods. A significant increase on the dynamic compressive strength, elastic modulus, and the dynamic tensile strength was found with the increase of the strain rate. The damage process and fracture pattern of the ZrB₂-SiC ceramic exhibited a significant strain-rate dependence under the dynamic compression. The strain rate-dependent elastic modulus and tensile strength were introduced into Johnson–Holmquist (JH-2) model to predict the dynamic compression behavior of the ZrB₂-SiC ceramic. The simulation results of the dynamic compressive strength, stress–strain relation, and fracture patterns were in good accordance with the dynamic experimental results.     

The compressive and tensile behavior of a 0/90 C fiber woven composite at high strain rates

An investigation into the compressive and tensile behavior of a carbon fiber reinforced resin matrix composite at high strain rates is carried out using a split Hopkinson bar. All the dynamic tests are performed under the condition of stress equilibrium and constant strain rate. The results of the compressive tests show that the failure strength and strain of the composite increase with the increase of strain rate. A plateau is observed in a typical stress–strain curve which prompts further study into the failure mechanism by monitoring the failure process with a high-speed camera. The three-phase failure mechanism of on-impact compression, crack-induced unloading, and crack deviation-caused further condensation, is found to have greatly increased the strength and toughness of the composite. In the tensile tests, an increase of strain rate produces a reduced fracture angle and extended crack path. In this process, more failure energy is absorbed, thus the failure strength and strain of the composite are improved. The Cowper–Symonds model of strain rate dependency indicates that the material has a higher tensile strength than compressive strength, and the strain rate sensitivity is more noticeable at high stain rates than quasi-static conditions.     

Triaxial strength and failure criterion of plain high-strength and high-performance concrete before and after high temperatures

Triaxial tests were performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength and high-performace concrete (HSHPC) at all kinds of stress ratios after exposure to normal and high temperatures of 20, 200, 300, 400, 500, and 600 °C, using a large static-dynamic true triaxial machine. Friction-reducing pads, using three layers of plastic membrane with glycerine were placed between the compressive loading plate and the specimens; the tensile loading planes of concrete samples were processed by an attrition machine, and then the samples were glued-up with the loading plate with structural glue. The failure mode characteristic of the specimens and the direction of the crack were observed and described. The three principally static strengths in the corresponding stress state were measured. The influence of the temperatures and stress ratios on the triaxial strengths of HSHPC after exposure to high temperatures was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease completely with the increase in temperature, the ratios of the triaxial to its uniaxial compressive strength are dependent on the brittleness-stiffness of HSHPC after different temperatures and the stress ratios. On this basis, a new failure criterion with the temperature parameters is proposed for plain HSHPC under multiaxial stress states. It provides the experimental and theoretical foundations for strength analysis of HSHPC structures subject to complex loads after subjected to a high temperature environment.     

Influence of the Fracture Criterion on the Failure Prediction of Ceramics Loaded in Biaxial Flexure

The failure probability of ceramic components in multiaxial stress states can be predicted from the results of uniaxial tests, if a suitable fracture criterion for multiaxial loading is known. In the paper it is investigated how the selected failure criterion influences the predicted distribution of the fracture stress of a component. Several acceptable failure criteria are found by comparing the results of four-point-bend tests performed with aluminum nitride with the results of concentric ring-on-ring tests.     

Analysis of multiaxial impact behavior of polymers

Impact performance is a primary concern in many applications of polymers. In this paper, finite element analysis (FEA) and ABAQUS/Explicit are used to simulate the deformation and failure of polymers in the standard ASTM D3763 multiaxial impact test. The specimen geometry and loading mode in this multiaxial impact test provides a close correlation with practical impact conditions. A previously developed constitutive model (“DSGZ” model) for polymers under monotonic compressive loading is generalized and extended for any loading mode and takes into account the different behavior of polymers in uniaxial tensile and compression tests. The phenomenon of thermomechanical coupling during plastic deformation is also included in the analysis. This generalized DSGZ model, along with thermomechanical coupling and a failure criterion based on maximum plastic strain, is incorporated in the FEA model as a coupled‐field user material subroutine to produce a unique tool for the prediction of the impact behavior of polymeric materials. Load‐displacement curves from FEA simulations are compared with experimental data for two glassy polymers, ABS‐1 and ABS‐2. The simulations and experimental data are in excellent agreement up to the maximum impact load. It is shown that not accounting for the different behavior of the polymer in uniaxial tensile and compression tests and thermomechanical coupling effects leads to an overestimation of the load and impact energy, especially at large displacements and plastic deformations. Friction also plays an important role in the impact behavior. If one neglects the friction between the striker and polymer disk, the predicted impact loads are lower as compared with experimental data at large displacements.     

Multiaxial Loading Fracture of Al2O3 Tubes: II, Weibull Theory and Analysis

The Weibull statistical fracture theory for multiaxial loading was developed for thick- and thin-walled tube geometries subjected to multiaxial loading in tension-internal pressure, compression-internal pressure, and pure torsion. As compared to uniaxial tension, lower strengths are predicted for tension-tension stress states and higher strengths for tension-compression stress states. Comparison to experimental results for A1₂0₃ tubes indicates a reasonable agreement with Weibull theory predictions for tension-internal pressure and compression-internal pressure conditions, but an underestimation of stress state effects in pure torsion. Results indicate a weakening effect of in-flaw-plane tensile stresses, with no observed influence of in-plane compressive stresses.     

A General Approach for the Statistical Analysis of Multiaxial Fracture

A general approach for the statistical analysis of fracture under multiaxial states of stress was developed. The approach invokes a critical coplanar strain-energy release-rate fracture criterion and considers distributions of penny cracks in random and preferred orientations. The analysis predicts strength ratios that depend on the strength dispersion and the proximity to the lower bound. For example, the uniaxial and equibiaxial strength ratios well above the lower bound are 1.25 to 1.09 for a typical range of dispersions. Uniaxial and equibiaxial fracture data for alumina were analyzed and compared with the theory. A good correlation was obtained.     

部分烧结陶瓷材料力学特性的DEM模拟

通过开展三维离散单元法数值模拟,考察了部分烧结陶瓷在单轴拉伸和压缩加载条件下的力学响应行为.模拟结果表明,拉伸加载下试样的破坏表现为裂纹"成核"效应,而压缩加载下则呈现为裂纹"聚并"效应;通过追踪固体键的断裂顺序和断裂模式发现,拉伸加载下固体键的破坏主要源于拉伸作用,而压缩加载下则为剪切作用.试样的宏观断裂强度与固体键...     

Compression behavior of woven glass/epoxy specimens using a new end‐loaded hybrid specimen

A new compression specimen was applied to woven glass/epoxy laminates. The specimen consists of epoxy layers cast on the sides of the laminate to prevent buckling. Thin‐sheet aluminum ends enable alignment and avoid crushing under end loading, which does not require any special fixture. The compression stress–strain behavior of the laminate was obtained from the specimens by discounting the previously measured stress–strain curve of the epoxy backings. Despite the higher scatter in compression tests, the average modulus was practically identical to the tensile modulus. Moreover, failure occurred away from the ends in nearly all of the specimens tested. The average compressive strength was 84% of the tensile strength and consistent with the flexural strength measured in four‐point bending tests. The present compression specimen could, therefore, become an interesting alternative to the more elaborate standard test methods available. Nevertheless, this new compression testing approach needs further evaluation involving application to other materials. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

Effects of stress during heating on strength and stiffness of concrete at elevated temperature

Concrete in structures exposed to high temperatures is practically always heated under stress. Yet, there are few experimental studies in which the concrete was heated under stress and then loaded to the peak, and most of these were performed under uniaxial compression. This paper reports on an experimental study of the effects of different heat–load regimes on the stress–strain behaviour of partially sealed concrete under multiaxial compression, at elevated temperature. The specimens were first heated (stressed/unstressed), then loaded to the peak in multiaxial compression. In contrast with previous experimental research, the results show that concrete heated under relatively low compressive stress has lower strength and stiffness than concrete heated without load. The results suggest that the presence of stress during first heating produces a specific damage, which could be the cause for a major component of the load induced thermal strain (LITS) in concrete.     

Dynamic compressive strength of alumina ceramics

Dynamic (220–510 s^?1) and quasi-static (0.001 s^?1) compression experiments are conducted on alumina ceramics implemented with two types of tungsten carbide inserts, cylindrical and step-shaped. Split Hopkinson pressure bar (SHPB) tests with in-situ, high-speed optical imaging are adopted to capture the damage and failure of ceramic samples under dynamic compression. The compressive strength of alumina ceramic samples with step-shaped inserts is 15%–30% higher than that with cylindrical inserts commonly used in previous studies, under both dynamic and quasi-static loading. Damage occurs first at the two ends of ceramic samples with the cylindrical inserts, followed by edge fracture and splitting cracks penetrating the sample. However, damage is initiated in the sample region away from the sample ends for the step-shaped inserts, and oblique and secondary transverse cracks dominate the failure process. The different damage modes in the case of step-shaped inserts result in the delayed damage initiation and sample failure, and consequently high compressive strengths. Finite element modelling (FEM) of the SHPB tests provides strength and damage evolution features consistent with the experiment using the Johnson–Holmquist (JH-2) model. FEM reveals equivalent, tensile and shear stress concentrations at the two ends of samples with cylindrical inserts. The stress concentrations are responsible for the damage initiation and growth at the sample ends and the following splitting cracks, consistent with the high-speed images. In contrast, homogeneous stress distributions are achieved in the sample with the step-shaped inserts, ensuring simultaneous damage development across the sample. Overall, the step-shaped inserts in conjunction with cylindrical samples can yield reliable strength measurements for ceramics and ceramic-like materials.     

Effect of Polyaxial Stress States on Failure Strength of Alumina Ceramics

The effect of polyaxial stress fields on the brittle fracture strength of polycrystalline alumina was investigated through the use of thin-walled cylinders. Combinations of internal pressure, external pressure, and axial loads produced stress states of tension-compression, tension-tension, and compression-compression. The failure envelope was generated for these stress states. The results indicated that biaxial tensile stresses reduced the strength of the material; however, the tensile strength increased at least 50% when a compressive stress existed normal to the tensile direction. Compression strengths as high as 640,000 psi were measured for a biaxial compressive stress state.     

Determination of the multiaxial failure criteria for alumina ceramics under tension–torsion test

Failure probability of ceramic components in multiaxial stress state can be predicted using the uniaxial test results (e.g. tension test, 4-point-bending test) when a suitable multiaxial criterion, which introduces the triaxiality of stress state, is known. In this article, tension–torsion tests were performed with alumina (Alsint 99.7) specimens from a standard manufacturer under two different load cases. Next experimental results were compared with the numerically calculated effective volume and effective surface values according to different multiaxial failure criteria. It was concluded that the specimens failed due to surface flaws and the normal stress criterion is the most appropriate criterion for the strength prediction of alumina ceramics under multiaxial stress state. Furthermore, it was shown that the Weibull modulus does not play a big role for the prediction of strength of alumina ceramics.     

Fracture of Al2O3 in Combined Tension/Torsion: II, Weibull Theory

The Weibull statistical fracture theory for multiaxial stresses has been extended to conditions of combined tension/torsion loading. At fracture, a tensile principal stress ratio σ₁ (tension/torsion) σ₁ (uniaxial tension) greater than one is predicted which is dependent on stress state, Weibull modulus, and fracture location. Comparison to experimental tension/torsion data for Al₂O₃ shows that the Weibull theory, although predicting correct trends, generally underestimates strengthening effects of the compressive principal stress, thus providing a conservative failure prediction. This discrepancy may be related to influences of stress state on crack-tip "process zone" behavior.     

Combined damaged elasticity and creep modeling of ceramics with wedge splitting tests

During the crack propagation in common refractory ceramics at high temperatures, creep may occur in the wake of a process zone and in front of a crack tip. To account for this phenomenon, an integrated material constitutive model was developed by combining the mechanical behavior following isotropic damaged elasticity concept and Norton-Bailey creep. The post peak fracture behavior followed the bilinear softening law and a simple criterion was defined to consider the creep asymmetricity in uniaxial tension and compression. The material constitutive model was applied to inversely identify mode I fracture parameters with wedge splitting tests of an alumina spinel material at 1200 °C. It showed that the mean ratio of the nominal notch tensile strength to the actual tensile strength was 1.93 and the mean pure fracture energy was 297.6 N/m. In addition, the creep contributed 12.9% on average into the total fracture energy.     

Effects of Crystal Orientation and Temperature on the Strength of Sapphire

The flexure and compressive strengths of sapphire are dependent on crystal orientation and temperature. Most notably, the c -axis compressive strength decreases below the tensile strength at temperatures >400°C and falls to 2% of the room-temperature compressive strength at 800°C. Loss of compressive strength complicates the interpretation of flexure tests. Four-point flexure specimens with no component of c -axis compression increase in strength at temperatures >500°C; however, specimens that have c -axis compression decrease in strength. It has been observed that c -axis compression causes twinning on rhombohedral crystal planes. Intersection of twins on different rhombohedral planes causes fracture that leads to mechanical failure.     

Experimental study of the material and bond properties of frost-damaged concrete

In an extensive experimental investigation, several types of tests were conducted on a reference specimen and frost-damaged concrete. Two levels of internal frost damage were quantified by the relative dynamic modulus of elasticity and compressive strength. Test results showed a significant influence of freeze–thaw cycles on the compressive strength and even more influence on the modulus of elasticity and the compressive strain at peak stress. Reduced tensile strength and increased fracture energy were measured. From inverse analysis of wedge splitting test results, a significant effect of frost on the shape of the tensile stress–crack opening relationship was observed: tensile strength was reduced, while the post-peak behaviour was more ductile for the frost-damaged concrete. Pull-out tests showed the influence of freeze–thaw cycles on bond strength and slip. The pull-out test results are compared with similar tests available in the literature and the effect of frost on bond behaviour is discussed.     

Deformation behavior of an epoxy resin subject to multiaxial loadings. Part I: Experimental investigations

The mechanical behavior of an epoxy resin (Epon 826) was studied by performing a series of tests on thin‐walled tubular specimens. These tests deal with different aspects of the mechanical behavior of this epoxy resin. The deformation behavior, such as viscoelastic behavior, hydrostatic stress effect, multiaxial behavior and loading path effect, was investigated. It was found that the Epon 826 epoxy resin is a highly nonlinear viscoelastic material. The effect of hydrostatic pressure on the deformation behavior of this epoxy is not significant. However, it shows different tensile and compressive deformation behavior. The loading path was found to have an observable effect on the deformation response of this epoxy, especially in the high stress/strain range.