率相关混凝土类材料SHPB试验的若干问题

对于断裂应变很小的混凝土类材料,在SHPB冲击试验中试样断裂前的应力是否达到均匀是冲击试验是否有效的一个关键。以水泥砂浆为例,采用弹性和ZWT粘弹性两种本构模型,通过特征线解法对高应变率SHPB试验过程中的加卸载应力均匀性进行了分析。发现入射波升时对脆性粘弹性材料的应力均匀性有影响,其中以τs/tL=2时最好,升时再延长反而对应力均匀化不利。采用不同升时加卸载时,应力幅值对于试样中应力均匀性没有影响,但对试样中应变和应变率的大小有影响。并且发现用常规的SHPB技术难以获得率相关脆性材料较可靠的应力-应变关系,但在应力均匀化后测得的动态断裂应力值是可靠的。     

Fatigue strength of the Cu/Si interface in nano-components

The fracture behavior of the Cu/Si interface in a nano-cantilever specimen with a 200 nm-thick Cu film (Specimen-200), which possesses a nanometer-scale strain-concentrated region, is examined under a cyclic bending load. The fatigue strength is around GPa level owing to the high yield stress of the Cu nano-film and the deformation constraint associated with the neighboring hard materials. The S-N curve shows clear dependence of fatigue life on the applied stress in the high-stress range, Δσ. Specimens with a 20 nm-thick Cu film (Specimen-20) are also investigated for comparison. The stress range in the fatigue fracture of Specimen-20 is higher than that of Specimen-200 for the same fatigue life. However, there is good coincidence in the Δσ/σ_s (σ_s: strength in monotonic load) vs. N_f (number of cycles to fracture) at high Δσ. The S-N curves suggest the existence of a fatigue threshold (Δσ_w) at low Δσ. The ratio of fatigue limit to the fracture stress in a monotonic loading, Δσ_w/σ_s, is large compared with the magnitude of bulk metal, which suggests the brittle behavior of the interface. Moreover, the fatigue limits have good coincidence with their yield stresses.     

Correlation between the accuracy of a SHPB test and the stress uniformity based on numerical experiments

Split Hopkinson pressure bar (SHPB) has become a frequently used technique to measure the uniaxial compressive stress–strain relation of various engineering materials at high strain rate. Using the strain records on incident and transmitter bars, the average stress, strain and strain rate histories within the specimen can be calculated by SHPB formulae based on one-dimensional wave propagation theory. The accuracy of a SHPB test is based on the assumption of stress and strain uniformity within the specimen, which, however, is not always satisfied in an actual SHPB test due to the existence of some unavoidable negative factors, e.g., friction and specimen size effects. Two coefficients are introduced in the present paper to measure the stress uniformity in axial and radial directions of the specimen in a numerical SHPB test. It is shown that the accuracy of a SHPB test can be correlated to these two stress uniformity coefficients. An assessment and correction procedure for SHPB test results is illustrated through a numerical example.     

Effects of radial inertia and end friction in specimen geometry in split Hopkinson pressure bar tests: A computational study

The split Hopkinson pressure bar (SHPB) technique has been used widely for the impact testing of materials in the strain-rate range from 10² to 10⁴ s⁻¹. However, some specific problems still remain mainly concerning the effects of radial inertia and end friction in a cylindrical specimen on the accurate determination of dynamic stress–strain curves of materials. In this study, the basic principle of the SHPB technique is revisited based on energy conservation and some modifications are made considering radial momentum conservation. It is pointed out that the radial inertia and end friction effects are coupled to each other in the SHPB specimen. Computational simulations using the commercial finite element (FE) code ABAQUS/Explicit ver. 6.8 are conducted to check the validity of the modifications for ductile pure aluminum specimens. Both rate-independent and rate-dependent models are adopted for the test material. Simulations are performed by varying two different control parameters: a friction coefficient between the specimen and the pressure bars and a slenderness ratio of the specimen (or thickness to diameter ratio).     

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part II: Numerical simulations

Split Hopkinson pressure bar (SHPB) tests have been used widely to measure the dynamic compressive strength of concrete-like materials at high strain-rates between 10¹ and 10³ s⁻¹. It has been shown in companion paper (Zhang M, Wu HJ, Li QM, Huang FL. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests Part I: Experiments. Int J Impact Eng 2009;36(12):1327–1334) that the axial strain acceleration is normally unavoidable in an SHPB test on brittle materials. Axial strain acceleration introduces radial confinement in the SHPB specimens and consequently enhances the compressive strength of concrete-like specimens. This paper employs numerical simulation to further demonstrate that the unexpected radial confinement in an SHPB test is responsible for the increase of the dynamic compressive strength of concrete-like materials at strain-rates from 10¹ to 10³ s⁻¹. It confirms the observations in Zhang et al. (Zhang M, Wu HJ, Li QM, Huang FL. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests Part I: Experiments. Int J Impact Eng 2009;36(12):1327–1334) that the dynamic increase factor (DIF) measured in SHPB tests can be reduced either by using tubular SHPB specimens or by reducing the diameter of the SHPB specimen. A kinetic friction model is proposed based on kinetic friction tests and is implemented in the numerical model. It shows that it is necessary to use a kinetic friction model, rather than a constant friction model, for more accurate numerical simulation of SHPB tests.     

SHPB测试中岩石试件应力均匀性分析研究

对花岗岩、千枚岩、磁铁石英岩三种岩石进行SHPB应力均匀性试验测试,研究表明:试件内达到应力均匀时间介于弹塑性状态假设条件下试件内达到应力均匀时间之间,且试件内达到应力均匀时间与二者的平均值具有一定的相关性。试验中子弹的冲击速度在一定范围内,能够使三种岩石满足应力均匀性的要求,且在断裂应变达到1%之前均有较长的恒应变率时间段。     

A critical assessment of high-temperature dynamic mechanical testing of metals

Determination of the mechanical properties of materials under the combined effects of high-temperatures and high strain-rates has been an important and challenging issue. A strategy has been proposed and evaluated recently towards this purpose in which a heating cell with accurate temperature control is synchronized with the split Hopkinson pressure bar (SHPB) system. This strategy allows pre-heating the specimen to desired temperatures before arrival of the stress wave and provides an experimental technique for the measurement of dynamic mechanical properties of materials at high-temperatures. Since its advent, this method has gained increasing interest in the community of dynamic mechanical testing owing to its ease of manipulation. However, a couple of critical problems should be addressed to validate the experimental results. Among the problems, a crucial one is associated with the temperature change in the heated specimen upon its contact with the relatively cold bars. In this paper, experiments were designed to determine the influence of cold-contact-time (CCT) on the temperature variation within the specimen. The experiments were conducted on Ti700 alloy at strain-rates of ∼10⁴ s⁻¹ and at temperatures from 20 to 800 °C. The results show that the CCT does have a strong effect on the experimental results. Based on the experimental results and our analyses, we believe that the data can faithfully reflect the material behavior if CCT is shorter than 50 ms. While in most systems without the heating cell being synchronized with the SHPB system, the typical CCT is about 500 ms, and therefore the experimental data cannot be taken as representing the material behavior.     

Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments

Effects of the inertia-induced radial confinement on the dynamic increase factor (DIF) of a mortar specimen are investigated in split Hopkinson pressure bar (SHPB) tests. It is shown that axial strain acceleration is unavoidable in SHPB tests on brittle samples at high strain-rates although it can be reduced by the application of a wave shaper. By introducing proper measures of the strain-rate and axial strain acceleration, their correlations are established. In order to demonstrate the influence of inertia-induced confinement on the dynamic compressive strength of concrete-like materials, tubular mortar specimens are used to reduce the inertia-induced radial confinement in SHPB tests. It is shown that the DIF measured by SHPB tests on tubular specimens is lower than the DIF measured by SHPB tests on solid specimens. This paper offers experimental support for a previous publication [Li QM, Meng H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test. Int J Solids Struct 2003; 40:343–360.], which claimed that inertia-induced radial confinement makes a large contribution to the dynamic compressive strength enhancement of concrete-like materials when the strain-rate is greater than a critical transition strain-rate between 10¹ and 10² s⁻¹. It is concluded that DIF formulae for concrete-like materials measured by split Hopkinson pressure bar tests need to be corrected if they are going to be used as the unconfined uniaxial compressive strength in the design and numerical modelling of structures made from concrete-like materials to resist impact and blast loads.     

Cracked Brazilian disc specimen subjected to mode II deformation

The centrally cracked Brazilian disc specimen has been used by many researchers to study mode I and mode II brittle fracture in different materials. However, the experimental results obtained in the past from this specimen indicate that the fracture toughness ratio (K_IIc/K_Ic) is always significantly higher than the theoretical predictions. It is shown in this paper that the increase in the ratio K_IIc/K_Ic can be predicted if a modified maximum tangential stress (MTS) criterion is used. The modified criterion takes into account the effect of T-stress in addition to the conventional singular stresses. The fracture toughness ratio K_IIc/K_Ic is calculated for two brittle materials using the modified criterion and is compared with the relevant published experimental results obtained from fracture tests on the cracked Brazilian disc specimen. A very good agreement is shown to exist between the theoretical predictions and the experimental results.     

Fracture behavior of nano-layered coatings under tension

The fracture of brittle/ductile multilayers composed of equal thicknesses of Si and Ag layers evaporated on a thick substrate is studied with the aid of a four-point bending apparatus. The system variables include individual layer thickness (2.5 to 30 nm), total film thickness (0.5 to 3.5 μm) and substrate material (polycarbonate, aluminum alloy and hard steel). The fracture is characterized by transverse cracks that proliferate with load. The crack initiation strain ε_i is virtually independent of total film thickness and substrate material while increasing with decreasing layer thickness h, to a good approximation as ε_i ~ 1/h^1/2. At higher strains, film debonding and buckling are evident.The fracture conditions are determined with the aid of a 2D finite element analysis incorporating the inelastic response of the interlayer. A fracture scenario consisting of tunnel cracking in the brittle layers followed by cracking in the interlayers is shown to be capable of predicting the observed increase in crack initiation strain with decreasing layer thickness. To realize this benefit the interlayer must be compliant and tough to force tunnel cracking in the brittle layers. The explicit relation for the crack initiation strain obtained from the analysis can be used to assess fracture toughness and improve damage tolerance in nanoscale layered structures.     

SHPB试验岩石试件应力平衡时间预估分析

运用一维应力波理论,对分离式Hopkinson压杆(SHPB)试验中弹性应力波的传播过程进行了分析,得到了试件应力分布相关计算公式,讨论了试件应力平衡时间的影响因素和变化规律。以变截面杆SHPB试验装置对煤矿岩石试件加载为例,计算分析了3种岩石试件在光滑的试验入射波和与其升时相同的理论梯形入射波加载情况下试件应力均匀性和应力平衡时间。发现采用变截面入射杆进行加载,能够实现岩石试件在应力峰值之前达到应力平衡,满足应力均匀性假定要求的有效条件。结果表明,采用理论梯形入射波可以近似代替与其升时相同的试验入射波,预估岩石试件应力均匀性和应力平衡时间,对类似脆性材料的SHPB试验设计具有一定的参考价值。     

A simplified expression for low cleavage probability calculation

This article describes an analysis made to develop a simplified stress-based criterion for brittle fracture focussed on the lowest probability of failure. For that, on the basis of fine numerical interpretation of two series of fracture-tests on 16MND5 reactor vessel steel, a number of variables were proposed:

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A stress threshold σ_th below which cleavage cannot occur. This stress is determined by testing on notch tensile specimen at low temperature.

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A minimum toughness K_min(T) required to make a crack unstable. The originality is here to consider this parameter depends on temperature.

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For K_J > K_min(T), a volume susceptible to cleavage, defined as the volume of material subjected to stress exceeding the threshold stress and noted V_th, representative of the fracture probability.

These three variables are explained in the article then used to establish a tentative criterion for expressing the risk of brittle fracture, in the presence or absence of a crack.     

Mixed mode fracture of a brittle orthotropic material—example of strongly textured zinc sheets

The response to mixed mode fracture of strongly textured sheets of impure zinc has been investigated using centrally cracked panels tested at 77 K. The specimens were designed such that the crack which was oriented at various angles to the tensile axis was always parallel to the basal plane direction. In this orthotropic material the strain energy release rate at fracture (G_c) is calculated using the analytical results published in the literature. The angular variation of G is calculated using the Nuismer's approximation. It is shown that the energy approach has some limitations as far as the prediction of mixed mode fracture in anisotropic materials is concerned. A local approach in terms of a combination of the resolved normal stress σ_n and the resolved shear stress (τ) applied to the basal slip plane is proposed to account for the fracture behavior of this material in mixed mode loading.     

On Influence of Non-Singular Stress States on Brittle Fracture

In the case of sufficiently brittle material the use of stress intensity factor as a fracture parameter alone is well justified within the Linear-Elastic Fracture Mechanics. This is because the singular stress field associated with the stress intensity factor is dominant near the crack tip. However, there are numerous experimental evidences that the critical stress intensity factor to cause fracture initiation (or fracture toughness) can be affected by the specimen geometry as well as loading conditions. To address this issue a number of twoparameter criteria have been proposed in the past, which often utilise non-singular terms of the classical asymptotic expansion of the stress field near the crack tip. Therefore, there is a problem of the selection of an appropriate parameter in addition to the stress intensity factor, which could account for various effects induced by the specimen geometry and loading on initiation of brittle fracture. This short paper demonstrates that brittle fracture conditions can be successfully predicted with various two-parameter criteria, and there are no clear advantages in the use of T-stress as the additional parameter in fracture criterion, in comparison with the next non-singular term, A ₁, of the asymptotic expansion.     

Stress–strain relationships of polycarbonate over a wide range of strain rate,including a shock wave regime

Stress–strain relationships of polycarbonate (PC) are determined over a very wide range of strain rates, including a shock wave regime. Plate impact tests, drop-weight tests, and quasi-static tests using universal and Instron testing machines are used for the high strain rate (10⁷ s⁻¹), medium strain rate (10² s⁻¹) and low strain rate (10⁻⁴ s⁻¹) tests, respectively. A newly modified unsteady wave sensing system (NM-UWSS) for plate impact tests is developed to determine the stress–strain relationships of PC. The system consists of a powder gun for plate impact tests, three embedded polyvenyliden fluoride (PVDF) gauges, and NM-UWSS. As originally proposed, UWSS is aimed at obtaining experimental inputs for the Lagrangian analysis used in determining the dynamic behavior of materials. We revise this standard system (UWSS) twice to gain a higher time resolution. In the past, the conventional charge mode (Q₂ method) was used. The first modified system (M-UWSS) has been used to study two classes of materials: (1) metallic materials and (2) polymeric materials, where the Q₁ method coupled with a transient differential equation for the equivalent circuit of the measurement circuit for the PVDF stress gauge was used. The latest method (Q_t method) for gaining the highest time resolution of shock wavefront structure by considering the effects of a piezofilm's thickness is proposed for PC at particle velocities of up to 1 km/s. Here we show from basic equations of piezoelectricity that the charge density q, i.e., the charge release per unit area, of the active electrode is proportional to the ratio of the thickness of the shocked region to the total thickness of the piezofilm. It is demonstrated that the rise time of shock charge density q in the piezofilm induced by such shock in the Q₂, Q₁ and Q_t methods, in this order, is becoming much shorter. The latest Q_t method has the highest accuracy among these three methods. Power law relations between stress and strain rate are observed again with PC under conditions of uniaxial strain over a very wide range of strain rates, i.e., 10⁻⁴–10⁷ s⁻¹ including a shock wave regime. For the PC, the effects of strain rate on the stress–strain relationships are estimated using empirical formula.     

Strain rate effects on viscoelastic crack bifurcation

The effects of applied strain rate on the viscoelastic crack bifurcation phenomenon in Polymethyl Methacrylate (PMMA) were investigated. It was still verified that the product $\text{σ}{}_{\mathrm{f}}\text{C}{}_{\mathrm{b}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was constant, as was already observed by Congleton and Petch, and Anthony, Chubb and Congleton, for brittle elastic materials, for any strain rate, where σ_f = the gross fracture stress and C_b= the main crack length until the bifurcation starts. However, it was found that the higher strain rate increases the main crack length C_b resulting in the decrease in the gross fracture stress σ_f and vice versa. This might be interpreted that the higher stress concentration at the initiation crack tip, which is realized by becoming more brittle due to the higher strain rate owing to the predominance of the elastic element in the viscoelastic material, decreases the gross fracture stress leading to the longer main crack length.     

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography.Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10⁻⁴ to 10³ s⁻¹ and tension tests at temperatures between −196 and 600°C.One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges.The other material fails in a ductile mode in all the investigated cases.     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.     

Dominant stress region for crack initiation at interface edge of microdot on a substrate

In order to examine the mechanics of crack initiation at the free interface edge of a microcomponent on a substrate, delamination tests are carried out for two specimen shapes of Cr microdots on a SiO₂ substrate. The microdots of the first specimen are shaped like the frustum of a round cone. The Cr microdots are successfully delaminated from the SiO₂ substrate in a brittle manner and the critical load is measured by atomic force microscopy (AFM) with a lateral loading apparatus. Stress analysis reveals that a singular stress field exists near the interface edge and the strength for the crack initiation is governed by the intensified normal stress field. The critical stress intensity parameter is evaluated as K_σC ≈ 0.24 MPa m^0.39. Similar delamination tests are conducted for microdots shaped like the frustum of an oval cone. The stress distributions at the crack initiation of this specimen shape show a higher normal stress than the first specimen shape in the region near the interface edge of about x < 40 nm, while it is lower in the region of about x > 50 nm (x: distance from the edge). This suggests a limitation of conventional fracture mechanics: namely, the crack initiation in these specimens is not uniquely governed by the intensity of the singular field. It is found that the delamination crack is initiated when the averaged stress σ_ya in the region of 90-130 nm reaches 190-270 MPa, regardless of the specimen shape. This indicates that the dominant stress region of crack initiation is roughly estimated as 90-130 nm and the criterion is given in terms of the averaged stress in the region.