High Strain Rate Compressive Tests on Woven Graphite Epoxy Composites

The behavior of composite materials may be different when they are subjected to high strain rate load. Penetrating split Hopkinson pressure bar (P-SHPB) is a method to impose high strain rate on specimen in the laboratory experiments. This research work studied the response of the thin circular shape specimens, made out of woven graphite epoxy composites, to high strain rate impact load. The stress-strain relationships and behavior of the specimens were investigated during the compressive dynamic tests for strain rates as high as 3200 s⁻¹. One dimensional analysis was deployed for analytical calculations since the experiments fulfilled the ratio of diameter to length of bars condition in impact load experiments. The mechanics of dynamic failure was studied and the results showed the factors which govern the failure mode in high strain deformation via absorbed energy by the specimen. In this paper, the relation of particle velocity with perforation depth was discussed for woven graphite epoxy specimens.     

Dynamic behaviour of UHMWPE yarns and addressing impedance mismatch effects of specimen clamps

The dynamic stress–strain behaviour of Spectra^® 900 yarns, made of highly oriented ultra-high molecular weight polyethylene (UHMWPE), is determined by means of a tensile split Hopkinson bar arrangement incorporating special grips to clamp the specimens. Test results show that a five-element viscoelastic constitutive model captures the behaviour of Spectra^® 900 yarns with good fidelity. Not uncommonly, as in this instance, grips used to clamp specimens introduce an impedance mismatch with the input/output bars, and the design of the clamps may not be amenable to modification to yield an impedance match. Consequently, an algorithm is developed to relate the strain signals from the input/output bars to what is experienced by the grips, and thus what is imposed on the specimen. This enables the extraction of corrected quantities for insertion into the Hopkinson bar equations. The proposed method is validated by finite element analysis.     

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).     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

An experimental method for dynamic tensile testing of concrete by spalling

A new application of the spalling phenomenon in long specimens is reported in this paper. The new experimental technique is based on an experimental setup which consists of an air launcher of cylindrical projectiles with a Hopkinson bar as a measuring tool and a relatively long concrete specimen in contact with the bar. The incident compression wave transmitted by the Hopkinson bar into the specimen is reflected as a tensile wave causing spalling. Although such configurations have been reported in the past, the main advantage of the present approach lies in the application of the detailed analysis, based on the wave mechanics with dispersion, to extract the specimen behaviour. Such an approach leads to an exact estimation of the local failure stress in tension at high strain rates, even above 100 s⁻¹. This paper demonstrates, using two series of tests on concrete, that this experimental setup can cover one decimal order of strain rates, from ∼10 to ∼120 s⁻¹. The tests performed at high strain rates on wet and dry concrete have indicated that the tensile strength is substantially influenced by the loading rate or strain rate. The absolute value of the failure stress for wet and dry concrete is almost the same for a particular strain rate, which does not occur when subject to low strain rates in tension or compression. A brief discussion is offered on a high rate sensitivity of concrete strength in tension at high strain rates.     

Dynamic splitting tensile properties of concrete and cement mortar

To investigate the dynamic tensile behaviours of concrete and cement mortar, a 50‐mm split Hopkinson pressure bar was applied on Brazilian disc specimens for dynamic tensile experiments, in which strain rate varied from 10^?5 to 20 s^?1. The high‐speed camera testing technique was used to capture the dynamic fractured process of the specimens at relative high strain rate. The experimental results revealed that the dynamic tensile strength of concrete specimens has a stronger strain rate effect than that of cement mortar specimens. Then three typical failure patterns of the specimens were confirmed in dynamic experiments. In addition, one‐parameter semi‐empirical relation between dynamic tensile strength and strain rate was established. Finally, the limitation of dynamic splitting experiments on Brazilian disc specimens was discussed in detail at high strain rate, in which the crack initiates from the contact point between the incident bar and specimens rather than the centre of the specimens.     

Calculation method for maximum low-cycle fatigue loads using FRASTA reconstruction data

A new method is proposed to calculate the load on a specimen during a fatigue failure using a post-mortem analysis of the fracture surfaces. This method uses the fracture-surface topography analysis to infer the plastic strains that have developed during the failure. That is, based on the previously proposed simple bar hypothesis, the fracture surfaces can be assumed to be composed of independent rectangular bars. After dividing the plastic deformation into single bars, the original lengths of these bars are calculated and then the global strains of these bars during the course of failure are calculated. According to the relationship between true stress and true strain for the material, the normal stress on the cross section of each bar is determined. Adding all loads on all bars together provides the total applied load of the specimen. As illustrations, the method is applied to fracture surfaces obtained from double-edge notched specimens made of two kinds of metallic alloy, broken under low-cycle fatigue. Results show that the calculated maximum fatigue load is almost equal to that recorded during testing.     

Effects of directional grain structure on impact properties and dislocation substructure of 6061-T6 aluminium alloy

Abstract

The effects of the grain structure direction on the impact properties and dislocation substructure of 6061-T6 aluminium alloy are investigated under room temperature conditions and strain rates of 1×10³, 3×10³ and 5×10³ s^?1 using a split-Hopkinson pressure bar system. The impact tests are performed using specimens machined from rolled 6061-T6 plates in the longitudinal, transverse and through thickness directions respectively. The results show that for all specimens, the flow stress increases with increasing strain rate. Furthermore, for all strain rates, the highest flow stress occurs in the transverse specimen. For strain rates of 1×10³ and 3×10³ s^?1, the flow stress in the through thickness specimen is greater than that in the longitudinal specimen. However, at a strain rate of 5×10³ s^?1, the flow stress in the longitudinal specimen is higher than that in the through thickness specimen due to a greater dislocation multiplication rate. For all three grain structure directions, the strain rate sensitivity increases with increasing strain rate, but decreases with increasing true strain. The highest strain rate sensitivity is observed in the longitudinal specimen at strain rates of 3×10³ to 5×10³ s^?1. The dislocation density increases markedly with increasing strain rate. Moreover, the square root of the dislocation density varies as a linear function of the flow stress in accordance with the Bailey–Hirsch relationship. The strengthening effect produced by the increased dislocation density is particularly evident in the transverse specimen, followed by the longitudinal specimen and the through thickness specimen.     

Quasistatic and dynamic crushability of polymeric foams in rigid confinement

An approach was developed for investigating the crushability behavior of epoxy-based, low-density structural polymeric foam (initial bulk density 0.81 g/cm³ was used for test illustration) under quasistatic and high strain rate conditions in rigid confinement. Quasistatic crushability tests were conducted in a steel confinement cell using an MTS material testing system and the high strain rate (dynamic) crushability behavior was investigated by placing a foam specimen in a steel confinement tube and then loading the specimen using two different split Hopkinson pressure bar systems, namely, a magnesium bar and steel bar. The dynamic deformation characteristics were obtained using a multi-step incremental loading procedure. It was found that these foams exhibited large uniform inelastic deformation during the confined loading. It is verified that multi-step incremental loading can be used to construct the complete stress–strain response curve for the specimens under both quasistatic and dynamic loading conditions. A phenomenological constitutive model was then applied to parametrically describe the crushability response and to determine the rate sensitivity of the foams. The rate sensitivity of yield stress was found to be around three under rigid confinement.     

Effects of strain rate on transverse tension properties of a carbon/epoxy composite: studied by moiré photography

The dependence on strain rate of the mechanical properties of a high performance carbon fibre/epoxy composite loaded in transverse tension has been investigated. Dog-bone shaped specimens have been tested in quasi-static and dynamic loading conditions. The dynamic tests were performed in a split Hopkinson bar at strain rates between 100 and 800 s⁻¹. A moiré technique combined with high-speed photography, at framing rates of 0.25–1 MHz, was used for extraction of the local strain fields. The transverse mechanical properties were found to have weak or no dependence on strain rate. The average transverse modulus did not depend on strain rate, whereas the strain to and stress at failure were found to increase slightly with increased strain rate. For these dog-bone shaped specimens the strain evaluated by conventional Hopkinson bar technique was found to underestimate the true strain field measured by moiré technique. Finally, the moiré technique facilitated crack-propagation monitoring in real time. Crack speeds up to 2300 m s⁻¹ were measured at transverse crack propagation.     

On the use of the non direct tensile loading on a classical split Hopkinson bar apparatus dedicated to sheet metal specimen characterisation

The facilities used to determine behaviour laws under dynamic loading are classified into two categories: impulsive and impact loading. For the first category, the properties of the industrial materials and their evolution at moderate strain rates range is generally obtained using split Hopkinson bars devices. Shear, tensile or compression strain modes, observed on crashed frameworks, are then applied on specimens to establish classical plastic stress/strain relations. Tensile testing using a non direct loading configuration raise the problem of the set-up and the holding of sheet specimens on the split Hopkinson bars devices, which generally induces impedance mismatches and perturbs the elastic pulses during their run through the specimen assemblies. This paper presents an original tensile testing configuration required bonded sheet metal specimens on the external part of threaded sleeves. A test programme is carried out on two metallic alloys (XES low carbon steel and 2024 T3 aluminium) at plastic strain rates between 180 and 440 s⁻¹. All results are compared with others experimental raw databases and validate this first stage of tensile loading.     

Subcritical crack propagation under cyclic stress impulse

An equipment has been designed to observe subcritical crack propagation under cyclic impulse (impact) loads. The equipment design uses the concept of stress wave propagation in bars. A four point bend notched specimen is struck by an incident bar with a known stress wave. The test specimens were machined from PMMA sheet (Lucite^®). The crack, initiated from the notch, was detected by a step wise increase of a graphitic grid imprinted on one side of the specimen. The data was analyzed using fracture mechanics theory and compared with that of conventional fatigue.Although the applied strain rate was quite high (1s^–1), stable crack propagation was significant. It appears that the elastic energy stored in the specimen within the duration of each impulse is dissipated in craze formation at the tip of the advancing crack. Furthermore, the magnitude of stable crack propagation was larger under impulse loading than under sinusoidal fatigue. On the other hand, cracks were slower under impulse loading. Fractographic evidence attributes these phenomena to the nature of craze growth under each loading condition.     

风机基础开孔板连接件剪切受力机理试验研究

鉴于目前国内出现了多台问题风机基础中穿孔钢筋疲劳脆断的工程事故,该文基于风机基础常采用的开孔板连接件构造,考虑多孔受力影响,共进行了4组12个开孔板连接件的推出试验以确定其抗剪承载力,并为其极端和运行工况设计提供依据。试验结果表明,穿筋试件的破坏过程大致分为3个阶段:①钢板与混凝土界面间摩擦受力阶段;②混凝土榫孔剪切受力阶段;③穿孔钢筋塑性剪断及其变形上方混凝土压溃。应变测试结果表明,由于穿孔钢筋的加入,上排孔的剪切受力使得下排穿孔钢筋弯曲受力明显,试件抗剪承载力较未穿筋试件得到显著提高;破坏阶段中,钢筋弯曲受力状态转变为孔内受剪,随着其上方混凝土的压溃,钢筋因受剪屈服退出工作;随着竖向裂缝的开展,全穿筋试件中3根钢筋均屈服,强度和塑性均得到有效的发挥,建议工程对中排、下排设置穿孔钢筋或三孔全设置。基于试验结果,针对不同构造的多孔推出试件破坏形态建立了多孔穿筋推出试件的抗剪承载力统一计算公式,计算结果表明计算值与试验值吻合较好,且偏于保守,可应用于实际工程。     

Anisotropic ductile failure in free machining steel at quasi-static and high strain rates

Leaded Free Machining Steel (FMS) specimens were tested in tension at quasi-static and high strain rates in both the longitudinal and transverse directions with respect to the axis of the bar material. For the quasi-static tests, a high degree of anisotropy of fracture behaviour was observed for both plain (unnotched) and notched specimens. However the difference in fracture strains for longitudinal and transverse directions was significantly reduced for the high stress triaxiality conditions produced by the sharper notches. Plain specimens tested at dynamic strain rates (10³ s⁻¹) failed at somewhat higher strains than those tested quasi-statically. For the notched specimens tested dynamically, there was a transition to a brittle mode of failure and there was no statistically significant anisotropy in the very low strains to failure recorded. These experimental results were linked to numerical predictions of the local stress, strain and strain rate conditions in the specimens carried out using a modified Armstrong–Zerilli constitutive model for the FMS. Changes in the percentage area and aspect ratio of the lead inclusions which act as sites for void growth under ductile failure conditions were measured for both longitudinal and transverse directions of loading. It was found that the apparent area of inclusions increases with degree of deformation due to void growth but that the aspect ratio decreases due to the inclusions/voids becoming more spherical. This effect was greater for loading in the transverse direction indicating that voids grow more readily from inclusions when the latter are aligned perpendicular to the direction of loading.     

Effects of prestrain and strain rate on dynamic deformation characteristics of 304L stainless steel: Part 1—Mechanical behaviour

Abstract

A split Hopkinson bar is used to investigate the effects of prestrain and strain rate on the dynamic mechanical behaviour of 304L stainless steel, and these results are correlated with microstructure and fracture characteristics. Annealed 304L stainless steel is prestrained to strains of 0·15, 0·3, and 0·5, then machined as cylindrical compression specimens. Dynamic mechanical tests are performed at strain rates ranging from 10² to 5 × 10³ s^-1 at room temperature, with true stains varying from 0·1 to 0·3. It was found that 304L stainless steel is sensitive to applied prestrain and strain rate, with flow stress increasing with increasing prestrain and strain rate. Work hardening rate, strain rate sensitivity, and activation volume depend strongly on the variation of prestrain, strain, and strain rate. At larger prestrain and higher strain rate, work hardening rate decreases rapidly owing to greater heat deformation enhancement of plastic flow instability at dynamic loading. Strain rate sensitivity increases with increasing prestrain and work hardening stress (σ-σ_y). However, activation volume exhibits the reverse tendency. Catastrophic fracture is found only for 0·5 prestrain, 0·3 strain, and strain rate of 4·8 × 10³ s^-1. Large prestrain increases the resistance to plastic flow but decreases fracture elongation. Optical microscopy and SEM fracture feature observations reveal adiabatic shear band formation is the dominant fracture mechanism. Adiabatic shear band void and crack formation is along the direction of maximum shear stress and induces specimen fracture.     

Influence of stress triaxiality and strain rate on the failure behavior of a dual-phase DP780 steel

To better understand the in-service mechanical behavior of advanced high-strength steels, the influence of stress triaxiality and strain rate on the failure behavior of a dual-phase (DP) 780 steel sheet was investigated. Three flat, notched mini-tensile geometries with varying notch severities and initial stress triaxialities of 0.36, 0.45, and 0.74 were considered in the experiments. Miniature specimens were adopted to facilitate high strain rate testing in addition to quasi-static experiments. Tensile tests were conducted at strain rates of 0.001, 0.01, 0.1, 1, 10, and 100 s⁻¹ for all three notched geometries and compared to mini-tensile uniaxial samples. Additional tests at a strain rate of 1500 s⁻¹ were performed using a tensile split Hopkinson bar apparatus. The results showed that the stress–strain response of the DP780 steel exhibited mainly positive strain rate sensitivity for all geometries, with mild negative strain rate sensitivity up to 0.1 s⁻¹ for the uniaxial specimens. The strain at failure was observed to decrease with strain rate at low strain rates of 0.001–0.1 s⁻¹; however, it increased by 26% for an increase in strain rate from 0.1 to 1500 s⁻¹ for the uniaxial condition. Initial triaxiality was found to have a significant negative impact on true failure strain with a decrease of 32% at the highest triaxiality compared to the uniaxial condition at a strain rate of 0.001 s⁻¹. High resolution scanning electron microscopy images of the failure surfaces revealed a dimpled surface while optical micrographs revealed shearing through the thickness indicating failure occurred via ductile-shear. Finite element simulations of the tests were used to predict the effective plastic strain versus triaxiality history within the deforming specimens. These predictions were combined with the measured conditions at the onset of failure in order to construct limit strain versus triaxiality failure criteria.     

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.     

An investigation on the dynamic response of polymeric,metallic, and biomaterial foams

Mechanical characterization of foams at varying strain rates is indispensable for the selection of foam as core material for the proficient sandwich structure design at dynamic loading application. Both servo-hydraulically controlled Material Testing System (MTS) and Instron machines are generally considered for quasi-static testing at strain rates on the order of 10⁻³ s⁻¹. Split Hopkinson pressure bar (SHPB) with steel bars is typically utilized for characterizing metallic foams at high strain rates, however modified SHPB with polycarbonate or soft martial bars are used for characterizing polymeric and biomaterial foams at high strain rates on the order of 10³ s⁻¹ for impedance match between the foam specimens and bars. This paper reviews the effect of strain rate of loading, density, environmental temperature, and microstructure on compressive strength and energy absorption capacity of various closed-cell polymeric, metallic, and biomaterial foams. Compressive strength and energy absorption capacity increase with the increase in both strain rate of loading and density of foams, but decrease with the increase in surrounding temperature. Foams of same density can have different strength and can absorb unequal amount of energy at the same strain rate of loading due to the variation of microstructure.     

Rate dependent deformation of carbon fibre reinforced Al–Li metal matrix composite

Abstract

The dynamic deformation characteristics and failure behaviour of laminated carbon fibre reinforced Al–Li metal matrix composite has been studied experimentally with the objective of investigating the dependence of mechanical properties on the applied strain rate and fibre volume fraction. A vacuum melting/casting process was used for manufacturing the tested composite. Impact testing was performed using a Saginomiya 100 metal forming machine and a compressive split Hopkinson bar over a strain rate range of 10^-1 s^-1 to 3×10³ s^-1. It is shown that the flow stress of the composite increases with strain rate and fibre volume fraction. The highest elongation to fracture values were found at low rate loading conditions, although a significant increase in ductility is obtained in the dynamic range. The composite appears to exhibit a lower rate of work hardening during dynamic deformation. Strain rate sensitivity and activation volume are strongly dependent on strain rate and fibre volume fraction. Fractographic analysis using scanning electron microscopy reveals that there is a distinct difference in the morphologies of the fractures, with corresponding different damage mechanisms, between specimens tested at low and high strain rates. Both strain rate and fibre volume fraction are important in controlling fibre fragment length and the density of the Al–Li debris. The relationships between mechanical response and fracture characteristics are also discussed.     

Dynamic material properties of wood subjected to low-velocity impact

This article studied the effects of low-velocity impact on the failure stresses and stiffness using a pendulum test. The specimens were of variable depth (20, 30, and 40 mm), a width of 50 mm, length of 650 mm, and span-length of 480 mm. The smallest specimen depth was similar to specimen sizes tested in the literature used to create the duration of load curve, while the largest specimen depth are considered structural size specimens. The impact was predicted using a numerical approach with Euler–Bernoulli beam, as well as Timoshenko beam theory, with a plastic contact law. The models were validated for impact from a low release-angle (where the beam remained elastic), but could use improvement for the force prediction at a high incidence velocity. The measured force signals were used as forcing functions to obtain the dynamic failure stresses for all of the evaluated specimens, and the Timoshenko–Goens–Hearmon Method to derive the dynamic E. The resulting strain rates ranged from 9.11?×?10^?5 s^?1 for the quasi-static specimens up to 25 s^?1 for the greatest incidence velocity. The results from this study suggest different duration of load factors than the Madison Curve, influencing the design of structures subjected to dynamic loading.