Effect of strain rate and saturation on uniaxial dynamic compressive behaviours of mortar

The effect of moisture content on the compressive mechanical behaviours of cement mortar under different high strain rates is studied in this paper. The rapid impact testing, i.e. the strain rates of 80, 100, 150, 200 and 250 s^? 1 by Split Hopkinson pressure bar, on number of specimens with special water/cement ratio of 0.50 and saturations as 0%, 25%, 50%, 75% and 100%, respectively, was executed. The dynamic compressive behaviours were analysed in terms of the maximum stresses, elastic modulus, critical strain at maximum stresses and ultimate strains at failure. Results indicated that similarity existed in the shape of strain–stress curves of mortars with different moisture subjected to different strain rates of impact loading, i.e. the upward section presented bilinear characteristics, while the descending stage was almost linear. As strain rate increases, the dynamic compressive strength, elastic modulus and critical strain at maximum stress increase which can be ascribed to the dynamic fracture effect and the microscope inertia effect. Besides, it was shown that desiccation provokes an increase in mortar strength and deformation behaviour of the studied mortar with different saturation caused by capillary depression and microcracking. Drying effect has to be considered in modelling of the coupling between desiccation and mechanical behaviour of the mortar. Finally, the multi-parametric statistical analysis of water content and strain rate on the mechanical behaviours of cement mortar subjected to dynamic loading is detailed.     

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.     

Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders

We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the effective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate‐independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular configuration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the fidelity of the model where rate effects are concerned. The model also predicts key features of the fracture pattern such as the primary lens‐shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size effect. These results validate the theory as it bears on mixed‐mode fracture and fragmentation processes in concrete over a range of strain rates. Copyright © 2000 John Wiley & Sons, Ltd.     

骨料粒径对混凝土动态拉伸强度及尺寸效应影响分析

骨料粒径是影响混凝土力学性能及破坏机理的重要因素。从细观角度出发,将混凝土看作由骨料颗粒、砂浆基质及界面过渡区组成的三相复合材料,考虑细观组分的应变率效应,建立了混凝土动态拉伸破坏行为研究的细观力学分析模型,模拟研究了不同骨料粒径下混凝土动态拉伸破坏行为,并揭示了动态拉伸强度的尺寸效应规律。研究表明:低应变率下骨料不发生破坏,骨料粒径对混凝土动态拉伸破坏模式及拉伸强度影响显著,且拉伸强度的尺寸效应随骨料粒径的减小而削弱;高应变率下裂缝将贯穿骨料,骨料粒径的大小对混凝土动态拉伸强度及尺寸效应影响可忽略。最后,结合应变率效应的影响机制,建立了混凝土拉伸强度的"静动态统一"尺寸效应理论公式,该公式可以较好描述各骨料粒径下混凝土动态拉伸强度与试件尺寸的定量关系。     

High Strain Rate Compressive Tests on Wood

Abstract: The penetrating split Hopkinson pressure bar was used to study the response of dry maple wood under high strain rate impact load. Using longer bar and shorter specimens utilised the assumption of one‐dimensional stress waves travelling along the bars and specimen because the experiment fulfilled the ratio of diameter to length of bars condition in Kolsky bar experiments. The stress–strain relationships and behaviour of the fibre structure materials’ failure were investigated during the compressive dynamic tests at strain rates between 950¹ and 2000 s^?1. The mechanics of dynamic failure was studied and it was confirmed that deformation of specimen is a linear function of energy absorption by specimens.     

Analysis of the strain-rate behavior of a basalt fiber reinforced natural hydraulic mortar

Fiber reinforced inorganic materials, such as concrete or mortars are expected to present good mechanical properties under high dynamic loading conditions, such as those induced by earthquakes. Furthermore, basalt fibers, which are being increasingly investigated in structural applications, are also expected to present good performance under high strain-rate conditions.This paper presents the results of a dynamic characterization of a basalt fiber reinforced natural hydraulic mortar, in order to verify its capability to withstand high dynamic loading conditions. In particular, the reinforced mortar was morphologically characterized by SEM and mercury intrusion porosimetry; then, quasi-static flexural and tensile tests were conducted. Finally, dynamic tensile failure tests were carried out at medium and high strain-rates, using a Hydropneumatic machine and a Modified Hopkinson bar apparatus, respectively. The results were elaborated to derive Dynamic Increase Factors for the tensile strength.The fiber addition leads to a bridge action effect, and consequently to a more ductile behavior and higher toughness of the fiber reinforced mortar compared to a plain mortar. In addition, the fiber reinforced mortar appears to be highly strain-rate sensitive, as the tensile strength DIF increased up to 5.1, for a high strain-rate of about 10² s⁻¹.     

Dynamic behavior of concrete at high strain rates and pressures: I. experimental characterization

Understanding the behavior of concrete and mortar at very high strain rates is of critical importance in a range of applications. Under highly dynamic conditions, the strain-rate dependence of material response and high levels of hydrostatic pressure cause the material behavior to be significantly different from what is observed under quasistatic conditions. The behavior of concrete and mortar at strain rates of the order of 10⁴ s⁻¹ and pressures up to 1.5 GPa are studied experimentally. The mortar analyzed has the same composition and processing conditions as the matrix phase in the concrete, allowing the effect of concrete microstructure to be delineated. The focus is on the effects of loading rate, hydrostatic pressure and microstructural heterogeneity on the load-carrying capacities of the materials. This experimental investigation uses split Hopkinson pressure bar (SHPB) and plate impact to achieve a range of loading rate and hydrostatic pressure. The SHPB experiments involve strain rates between 250 and 1700 s⁻¹ without lateral confinement and the plate impact experiments subject the materials to deformation at strain rates of the order of 10⁴ s⁻¹ with confining pressures of 1–1.5 GPa. Experiments indicate that the load-carrying capacities of the concrete and mortar increase significantly with strain rate and hydrostatic pressure. The compressive flow stress of mortar at a strain rate of 1700 s⁻¹ is approximately four times its quasistatic strength. Under the conditions of plate impact involving impact velocities of approximately 330 ms⁻¹, the average flow stress is 1.7 GPa for the concrete and 1.3 GPa for the mortar. In contrast, the corresponding unconfined quasistatic compressive strengths are only 30 and 46 MPa, respectively. Due to the composite microstructure of concrete, deformation and stresses are nonuniform in the specimens. The effects of material inhomogeneity on the measurements during the impact experiments are analyzed using a four-beam VISAR laser interferometer system.     

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.     

Toughness of fibre reinforced hydraulic lime mortar. Part-2: Dynamic response

The seismic rehabilitation of historical masonry buildings necessitates a quantitative understanding of the repointing mortar under variable strain rates. In Part-1 of this paper, plain and fibre reinforced hydraulic lime mortar specimens were examined under compression, flexure and direct shear to evaluate the post-crack response under quasi-static loading. It was seen that although the fibres enhance the flexural toughness of hydraulic lime mortar, the material is weakest in Mode I fracture. In Part-2 of this paper, the authors describe the strain rate sensitivity of hydraulic lime mortar on the basis of impact testing of notched beams. The mixes were identical to those examined in Part-1, and the dynamic response was evaluated using a drop-weight impact machine for strain rates in the range of 10^?6 to 10 s^?1. The authors found that compared to fibre reinforced Portland cement-based mortar and concrete, the flexural response of hydraulic lime mortar is more sensitive to strain rate.     

Influence of Shock Pre‐Compression Stress and Tensile Strain Rate on the Spall Behaviour of Mild Steel

Abstract: A series of plate‐impact spall experiments were conducted to investigate the influence of shock pre‐compression stress and tensile strain rates on the dynamic tensile fracture (or spall) behaviour of shocked mild steel. The shock pre‐compression stress amplitude and tensile strain rate were controlled independently to ensure that only one single‐loading parameter varied for each experiment. A push–pull type velocity interferometer system for any reflector (VISAR) was used to measure the free surface velocity profiles of samples. It is observed from experimental results that the influence of shock pre‐compression stress amplitude on the spall strength is less significant in the range attained in these experiments, whereas with increasing tensile strain rate, an evident 65% increase of spall strength is determined in the present tensile strain rate range of 10⁴ to 10⁶ s^?1. VISAR data are compared with finite‐difference calculations employing a modified damage function model with a percolation–relaxation function, and a good agreement between the calculation and the experiments was obtained. Preliminary simulation results also revealed that a critical damage exists, which physically corresponds to the critical intervoid ligament distance for triggering the onset of void coalescence, and may be regarded as a material parameter for describing the dynamic tensile fracture and independent of the loading conditions.     

Study on mechanical properties and constitutive model of 5052 aluminium alloy

The stress–strain relationship of 5052 aluminium alloy was investigated via quasi-static tensile tests and split Hopkinson pressure bar tests. The specimens were exposed to various temperatures (25–500°C) and strain rates (10^?4–0.7?×?10^4?s^?1). At strain rates ranging from 0.001 to 3000?s^?1, the material underwent significant work hardening. When the strain rate exceeded 5000?s^?1, the work hardening effect decreased and the flow stress was relatively constant. The Johnson–Cook constitutive model was modified to describe the deformation behaviour of the material subjected to high temperatures and strain rates. The accuracy of the modified model was verified through ballistic impact testing.     

Study of Dry and Wet Cement Mortar Dynamic Properties

We performed dynamic tests and studied the dynamic properties under compression of dry and wet cement mortar specimens using the Hopkinson split pressure bar method. As a result, we determined the fracture stresses and their dependence on the applied loading growth rate. It is noteworthy that the strength characteristic of wet material under study is less by 10–15% as compared to the dry one.     

Influence of free water content on the compressive mechanical behaviour of cement mortar under high strain rate

The effect of free water content upon the compressive mechanical behaviour of cement mortar under high loading rate was studied. The uniaxial rapid compressive loading testing of a total of 30 specimens, nominally 37 mm in diameter and 18.5 mm in height, with five different saturations (0%, 25%, 50%, 75% and 100%, respectively) were executed in this paper. The technique ‘Split Hopkinson pressure bar’ (SHPB) was used. The impact velocity was 10 m/s with the corresponding strain rate as 10²/s. Water-cement ratio of 0.5 was used. The compressive behaviour of the materials was measured in terms of the maximum stress, Young’s modulus, critical strain at maximum stress and ultimate strain at failure. The data obtained from test indicates that the similarity exists in the shape of strain–stress curves of cement mortars with different water content, the upward section of the stress–strain curve shows bilinear characteristics, while the descending stage (softening state) is almost linear. The dynamic compressive strength of cement mortar increased with the decreasing of water content, the dynamic compressive strength of the saturated specimens was 23% lower than that of the totally dry specimens. With an increase in water content, the Young’s modulus first increases and then decreases, the Young’s modulus of the saturated specimens was 23% lower than that of the totally dry specimens. No significant changes occurred in the critical and ultimate strain value as the water content is changed.     

低应变率下混凝土动态拉伸破坏尺寸效应细观模拟

在混凝土静态破坏尺寸效应方面已取得了较完善的成果,而在动态破坏尺寸效应方面,包括其产生机制及对应的尺寸效应律的研究则非常匮乏。为探讨动态荷载作用下混凝土尺寸效应行为,从细观角度出发,结合混凝土细观结构特征,考虑动态加载下细观组分应变率效应的影响,建立了混凝土破坏行为研究的细观力学分析模型与方法。以双边缺口混凝土试件为例,对其在低应变率（10-5 s-1~1 s-1）下混凝土动态拉伸破坏行为及尺寸效应进行细观数值模拟,并分析了应变率效应对动态破坏尺寸效应的影响。最后,结合应变率效应对强度及尺寸效应的影响规律—“强度增强效应”与“尺寸效应削弱效应”,在静态破坏尺寸效应律的基础上,建立了混凝土拉伸强度的“静动态统一”尺寸效应理论公式,并验证了理论公式的准确性和合理性。     

Investigating the static and dynamic tensile mechanical behaviour of polymer‐bonded explosives

The tensile properties of a polymer‐bonded explosive (PBX) were systematically studied by using quasi‐static and dynamic experiments. A non‐linear constitutive relation was developed to describe the tensile behaviour of the PBX. The tensile properties of the PBX under different strain rates and temperatures were measured in quasi‐static tests. The tensile behaviour of the PBX was found to exhibit high strain rate and strong temperature dependence, attributable to the large fraction of the polymer binder. To obtain the rational dynamic tensile results, a modified split Hopkinson tensile bar (SHTB) setup was designed such that the specimens were in dynamic stress equilibrium and deformed homogeneously at nearly constant strain rates. To characterise the viscoelastic behaviour, the master modulus curve was derived from the tensile stress relaxation tests at different temperatures. The non‐linear constitutive model was implemented in ABAQUS to predict the tensile behaviour of the PBX. The computational results were found to be in good agreement with the experimental results.     

The response of masonry joints to dynamic tensile loading

This paper presents results from laboratory tests on masonry joints subject to dynamic tensile loading. The tests were carried out using?specially designed Split Hopkinson Pressure Bar apparatus, the development of which is also?briefly described in the paper. It was found experimentally that there was a significant apparent dynamic enhancement in the tensile strength when specimens were loaded at strain rates of approximately 1 s^?1. (Dynamic Increase Factor = 3.1). Finite element modelling has been used to support a conjecture that this effect may?at least partly be a result of the inherent spatial variability of the brick–mortar bond strength, rather than being a genuine material characteristic per se.     

纤维高强混凝土的动态力学性能试验研究

为研究纤维高强混凝土材料在冲击荷载下的动态压缩性能,采用大尺寸φ75mm Hopkinson压杆,对三种纤维含量的钢纤维高强混凝土、PVA纤维高强混凝土试件进行了三种应变率范围的冲击压缩试验,得到了它们在较高应变率范围内的动态应力-应变关系。试验表明纤维高强混凝土材料为应变率敏感性材料,在较高应变率范围内纤维高强混凝土材料的动态应力-应变关系是与应变率相关的。纤维高强混凝土材料的破坏应力和破坏应变随应变率的增大而增大。钢纤维和PVA纤维对混凝土耗能能力的改善和提高表现在材料达到峰值应力后开始破坏的过程中。同时也对两种纤维高强混凝土材料的纤维增韧特性及耗能机理也进行了分析和探讨。     

Static and dynamic compression strength of hot-pressed boron carbide using a dumbbell-shaped specimen

Dumbbell-shaped specimens were machined from a tile of a commercially available boron carbide and subjected to static and dynamic compressive loads. Static experiments were performed using a screw-driven load frame, and the fracture process was recorded with a high-speed camera. Dynamic experiments were performed using a split-Hopkinson pressure bar and an ultra-high-speed camera to record the fracture process. The average static (~10^?1 s^?1) compressive strength of this boron carbide was determined to be 6.1 ± 0.3 GPa, and the dynamic compression strength, up to a strain rate of 300 s^?1, was 6.2 ± 0.3 GPa. These strength values are twice the value reported by the manufacturer and approximately 30% higher than the values reported by others for the same boron carbide but when using a cuboidal specimen geometry.     

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.     

Ultra‐High‐Speed Full‐Field Deformation Measurements on Concrete Spalling Specimens and Stiffness Identification with the Virtual Fields Method

Abstract: For one decade, spalling techniques based on the use of a metallic Hopkinson bar in contact with a concrete sample have been widely employed to characterise the dynamic tensile strength of concrete at strain rates ranging from a few tens to hundreds of s^?1. However, the processing method based on the use of the velocity profile measured on the rear free surface of the sample (Novikov formula) remains quite basic. In particular, the identification of the whole softening behaviour of the concrete material is currently out of reach. In the present paper, a new processing technique is proposed based on the use of the virtual fields method (VFM). First, a digital ultra‐high‐speed camera is used to record the pictures of a grid bonded onto the specimen. Then, images of the grid recorded by the camera are processed to obtain full‐field axial displacement maps at the surface of the specimen. Finally, a specific virtual field has been defined in the VFM equation to use the acceleration map as an alternative ‘load cell’. This method applied to three spalling tests with different impact parameters allowed the identification of Young's modulus during the test. It was shown that this modulus is constant during the initial compressive part of the test and decreases in the tensile part when microdamage exists. It was also shown that in such a simple inertial test, it was possible to reconstruct average axial stress profiles using only the acceleration data. It was then possible to construct local stress–strain curves and derive a tensile strength value.