Bimaterial Specimens Research Articles

Energy release rate in bimaterial specimens tested in pure modes I and II

New closed-form analytical expressions of the energy release rate of a bimaterial cracked specimen are derived, when it experiences pure mode I in an asymmetric double cantilever test, and pure mode II in an asymmetric end-notched flexure test. The analysis is based on the strain coenergy and on the laminated beam theory. The results of the analytical approach are compared with those obtained using the finite element method in two ways: by the virtual crack closure technique at a test point and by cohesive elements during a virtual delamination test. The agreement is excellent in both cases.

Modeling of 2D thermo-elastic brittle fracture using smoothed floating node method

This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity.

A robust staggered localizing gradient enhanced isotropic damage model for failure prediction in heterogeneous materials

In the present work, a robust and efficient staggered localizing gradient damage model (LGDM) with a simple isotropic damage variable is adopted to predict crack growth phenomena in bi-material and fiber reinforced composites under mixed-mode loading. We first consider a series of three-point bend experiments conducted by Lee and Krishnaswamy (2000) on bi-material specimens of PMMA/Al6061, where the staggered LGDM is shown to capture correct crack profiles under different boundary conditions. It is observed that the numerical crack paths are well compared with the experimental crack paths. Next, a fiber reinforced composite with a central fiber is considered where the effect of change in fiber sizes on the overall structural responses is investigated. It is seen that the increasing fiber size results in reduced load carrying capacity of fiber reinforced composites. Finally, we consider a fiber reinforced composite with fibers located on opposite edges of the specimen. Here, a parametric study on the strength ratio of the matrix phase is conducted to investigate their effect on crack initiation, propagation, and orientation. These simulations highlight the predictive capability of the present model in terms of structural responses as well as sharp crack profiles.

An experimental analysis of crack terminating perpendicular to the bimaterial interface under varying mode mixities

SIFs for crack terminating perpendicular to the interface of a bimaterial subjected to varying mode mixities are evaluated with a novel bimaterial specimen using the experimental technique of photoelasticity. A simple form of multiparameter equation defining the stress field for the crack terminating at the interface at an arbitrary angle along with the details on interfacial SIF and combined SIF for a bimaterial problem are brought out. The stress field equation is incorporated in an in-house developed PSIF software as a separate problem module for the determination of crack tip stress field parameters using a non-linear least squares methodology. A compact bimaterial Brazilian disc specimen with crack in one of the material sides terminating perpendicular to the interface and at an arbitrary angle to the point of loading, is considered for the study. SIFs of two such specimens, a polymer–polymer pair, and a metal-polymer pair with two different bimaterial constants are determined. The normalized SIF values are evaluated as a function of crack orientation angles. The SIF values for the metal-polymer pair were found to be higher compared to the polymer–polymer interface. The peak values of SIFs are observed at a crack orientation angle of 30°. At orientation angles close to 0° and 90°, the SIF values were less pronounced.

Layer-level AISI 316L-18Ni (300) Maraging multi-material fabrication via Laser-Powder Bed Fusion

Overcoming most of the limitations of conventional subtractive techniques, Laser-Powder Bed Fusion (L-PBF) is a widely adopted technology that allows the fabrication of metallic components with complex geometries. Available machines can work with a large variety of materials; however, multi-material printing is limited to inter-layer fabrication, i.e., each layer is made out of a single material. In this work, we aim at expanding the multi-layer printing capabilities of L-PBF to intralayer manufacturing (i.e., two different materials in the same layer), overcoming the previous limitations. To investigate the effectiveness and validate the proposed method, two widely used steels are used as powders to manufacture bi-material specimens, i.e., the AISI 316L austenitic stainless steel and the 18Ni (300) Maraging steel. Based on metallurgical and mechanical testing evidence, the results show that the method is repeatable and capable of fabricating strong and tough intralayer interfaces. While weak interfaces between materials with rather different mechanical properties are common in multi-material printing techniques, our method allows us not only to produce bi-materials with stronger interfaces but also to reduce discontinuities to those normally found in additive manufactured components. These results are obtained without any modifications to the machine and with low-cost additional equipment, opening the way for easy and cost-effective implementation.

Effects of thermal treatment on the fracture behavior of rock-concrete bi-material specimens containing an interface crack

The study of the fracture characteristics of rock-concrete structure containing an interface crack under high temperature is vitally significant for the durability and stability assessment of concrete construction projects on rock foundations. Brazilian splitting tests were performed on rock-concrete cracked straight-through Brazilian disc (CSTBD) specimens after different heat treatment temperatures. The crack extension process of the specimen was analyzed using digital image correlation (DIC) technique. The effects of temperature, interface crack inclination and concrete strength on fracture characteristics were investigated. The results indicate that at high temperatures, free water and structural water escape from rock and concrete, and crystal structure of the mineral composition is altered, which induces the development of internal pores and microcracks in the material and weakens the mechanical properties. The specimen displays brittle fracture behavior at 25 °C-300 °C, and plastic fracture behavior at 500 °C-700 °C. The wing crack extension in concrete (weak material) occurs preferentially, and this phenomenon becomes more apparent with raising temperature. When α ≤ 45°, the length of crack extension along the interface increases with increasing temperature, while when α > 45°, the increase in temperature makes the crack initiation closer to the disc center. The fracture energy and the difference in fracture energy between varying inclinations decrease with raising temperature. Furthermore, temperature has an essential impact on fracture toughness. As temperature increases, the fracture toughness generally decreases, the difference in mixed fracture toughness between different inclination angles gradually increases, and the fracture propagation resistance weakens.

Mode decoupling in interlaminar fracture toughness tests on bimaterial specimens

The present work has a two-fold objective: (i) to critically review the methods for fracture mode decoupling in unconventional laboratory specimens, such as the asymmetric double cantilever beam (ADCB) specimen; and (ii) to propose mode decoupling conditions and associated specimen design formulae to obtain pure fracture modes when bimaterial specimens are tested in ADCB and asymmetric end-notched flexure (AENF) configurations. In the first part of the paper, the literature on fracture mode decoupling is reviewed to shed light on some controversial points. We start with discussing various pure-mode conditions suggested by different authors and continue with the simplest case of the bimaterial joint. Our review also considers complex cases, such as the presence of bending–extension coupling or residual (hygrothermal) stresses. In the second part of the paper, bimaterial specimens loaded in ADCB and AENF test configurations are investigated. Employing energetically orthogonal mode decomposition, Engesser–Castigliano’s theorem, and the laminated beam theory, we illustrate specimen design criteria enabling to obtain pure fracture modes. The obtained specimen design formulae are validated through finite element analyses.

Interfacial fracture performance of engineered cementitious composites and fire-damaged concrete

This study investigated the interfacial fracture properties of engineered cementitious composites (ECC) and fire-damaged concrete using bi-material wedge splitting specimens. The full load versus crack mouth opening displacement (CMOD) curves of the bi-material specimens were obtained using wedge splitting tests, and the fracture toughness and fracture energy were calculated. The effects of the maximum temperature experienced by the concrete (20–700 °C) and the interfacial roughness (0–5 mm) on the interfacial damage mode, fracture toughness, and fracture energy were studied. The results indicated that when the maximum temperature experienced by the concrete was lower than 400 ℃ or the interface was smooth, the damage mode of the specimens was primarily adhesive failure. However, when the maximum temperature experienced by the concrete was equal to or greater than 400 °C and the interface was rough, cohesive failure often occurred in the specimens. Owing to the change in the damage mode, the bi-material specimens had the highest values of the fracture toughness and fracture energy at 400 °C. When the maximum temperature experienced by the concrete exceeded 400 °C, both the fracture toughness and fracture energy decreased with the increasing temperature. In this study, the fracture toughness and fracture energy of the bi-material specimens first increased and subsequently decreased with the increaseing roughness, and the maximum fracture toughness and fracture energy values were obtained when the interface roughness was 3 mm. The study results would provide a reference for the surface treatment when ECC was used in the strenthening of fire damaged concrete.

Early-age fracture behavior of sandstone-concrete interface with different sand/cement ratios

To understand the influence of sand/cement (S/C) ratio on the mode I fracture characteristics of the sandstone-concrete interface (SCI) at different ages, the quasi-static three-point bending test was carried out on semi-circular bi-material specimens. Experimental results indicate that the fracture toughness (KIC) of SCI increases first and then decreases with the increase of S/C ratio. Furthermore, when the age of concrete is between 0.5 and 7 days, the fracture energy (Gf) of SCI with different S/C ratios fall in the following order: G1.0>G0.0>G3.5. However, when the age of concrete ranges from 14 to 28 days, the order of fracture energy is changed to G3.5>G1.0>G0.0. Additionally, many obvious acoustic emission signals appear before the final failure of the specimen when the S/C ratio is 3.5. However, when the S/C ratios are 0.0 and 1.0, only few apparent acoustic emission signals appear at the final failure. In addition, when the S/C ratios are 0.0 or 1.0, the load–displacement curve of specimens in the age interval [0.5d, 28d] has one single peak point. However, when the S/C ratio is 3.5, the load–displacement curve of specimens in the age interval [7d, 28d] shows double-peak points. Moreover, the S/C ratio also controls the failure pattern of SCI. Compared to those with S/C ratios of 0.0 and 1.0, the broken concrete or rock with S/C ratio of 3.5 is more dispersed.

Cracking behavior of concrete/rock bi-material specimens containing a parallel flaw pair under compression

Crack propagation and coalescence of pre-existing flaws in concrete/rock bi-material are critical for stability assessments of rock/concrete structures. A hybrid finite-discrete element method (FDEM) was used to simulate the cracking behavior of the concrete/rock bi-material containing a parallel flaw pair under compression. The model was validated by physical tests. The results indicate that the crack evolution does not occur synchronously in the concrete and rock layers. The cracks in the different material layers penetrate the interface and coalesce at lower interface dip angles, whereas an interface crack always forms at higher interface dip angles, preventing crack coalescence in different material layers. A threshold of the strength ratio exists and determines whether the cracks in different material layers coalesce. If the strength ratio is lower than the threshold, the crack propagations are limited to one material due to the interface crack. If the strength ratio exceeds the threshold, the cracks in the different materials penetrate the interface and coalesce. Two critical values of the interface reduction coefficient exist for a given interface dip angle. The cracking pattern of the bi-material can be classified into cracking along the interface, local cracking in the different materials, and crack coalescence in different materials.

Dynamic fracture behavior and fracture toughness analysis of rock-concrete bi-material with interface crack at different impact angles

The crack initiation and propagation behavior of interface crack under impact are of great significance for evaluating the stability of rock-concrete system and other layered structures. Dynamic test using split-Hopkinson pressure bar (SHPB) system was performed on bi-material cracked straight-through Brazilian disc (CSTBD) specimens, and the fracture processes of specimens were monitored by means of a high-speed camera. The effects of the impact angle, concrete strength and strain rate on the dynamic fracture behavior were investigated. The results show that three typical fracture types can be identified: interface fracture, combined fracture (interface/shear and tension fracture) and tensile fracture. The interface fracture appears under small impact angle, while the combined fracture occurs with the further increase of impact angle. The crack initiation time of wing cracks and the number of secondary cracks are mainly affected by the strength of concrete in the bi-material specimen. Crack initiates earlier and more secondary cracks are generated in concrete material (weak material), and the number of secondary cracks increases with increasing strain rate. The dissipated energy increases gradually as the impact angle increases from 0° to 75°, while it decreases when the impact angle exceeds 75°. As the concrete strength increases, the difference in dissipated energy for different impact angles decreases. Furthermore, the effects of impact angle, concrete strength and loading rate on the dynamic fracture toughness for different loading modes are also discussed. The results indicate that the normalized stress intensity factors (SIFs) at the two tips of the interface crack are distinct and the difference increases with increasing crack length-to-diameter ratio. The impact angle, concrete strength and loading rate influence the dynamic fracture toughness significantly.

Experimental and numerical study on the ductile fracture response of X65 girth-welded joint made of Inconel 625 alloy

This work presents an experimental/numerical study characterizing the ductile fracture response of a pipeline girth weld of a corrosion-resistant alloy, Inconel 625. The welded joint was prepared with a narrow gap geometry. Thus, a newly designed double-groove bar is used to measure the weld metal’s tensile stress–strain curve. The geometry is extracted directly from the girth weld joint reducing the manufacturing process of tensile weld samples. The tensile result obtained from the bimaterial specimen is used to calibrate the modified Mohr–Coulomb damage model. A critical strain locus is defined for both materials, X65 and Inconel 625, depending on the stress triaxiality and Lode angle. A post-softening law is implemented to model the stable crack extension. The damage model is coded in a VUMAT subroutine in Abaqus software. The post-softening response is calibrated using a fracture toughness test. Then, validations are performed using a bimaterial specimen with a single groove and a bending fracture specimen. Overall, the matching is good between numerical and experimental results. Finally, numerical tests are performed for circumferential defective welded pipes to understand the influences of combined loads and misalignment on the pipe’s strain capacity. For partially undermatched weld joints, a flat double-groove bar is recommend for measuring the tensile mechanical properties of narrow gap welds. The CTOD-R curve measured at the FEM node behind the initial crack tip matches well the experimental CTOD based on the J-integral.

Discrete element modeling of rock-concrete bi-material discs under dynamic tensile loading

As the most fragile component in a bi-material, the performance of the rock-concrete interface can greatly affect the stability and durability of the concrete structures founded on the rock masses. In this study, a range of numerical simulations using the discrete element method (DEM) have been conducted to identify the failure mechanism and mechanical property of the rock-concrete bi-materials under the dynamic flattened Brazilian disc (FBD) tests using the modeled split Hopkinson pressure bar (SHPB) system. There are four groups of bi-material specimens that differ in the aspects of rock type (i.e. limestone and sandstone), interface inclination (i.e. 0°, 15°, 30°, 45°, 60°, 75°, and 90°), and specimen configuration (i.e. intact and hollow). The numerical results show that the nominal tensile strength depends on the rock type, and the intact specimen has a higher loading capacity than that of the hollow specimen. The failure modes are classified into three main types in intact limestone-concrete bi-materials according to the degree of the interface angle, which is in good agreement with the previous experimental results. Such transition from interface failure to tensile failure can be observed as well in the bi-material specimens with a hole inside, while the varying inclination angle has a minimal effect on the failure pattern of the sandstone-concrete bi-material specimens. The cracking process of the specimens is visualized using the evolution of acoustic emission (AE) activities. The moment tensor inversion interprets that more energy is required for cracks to propagate from concrete to limestone. The overall AE magnitude is the lowest in limestone-concrete specimens with a pre-cut opening due to the deteriorated specimen bearing capacity.

A shooting approach to the scaled boundary finite element equations of elastodynamics in the frequency domain

Dealing with numerical analysis of problems, especially ones with semi-infinite boundaries, scaled boundary finite element method has emerged as one of the efficient tools for the task. Combining the exactness of strong forms with the flexibility of weak formulations makes the method an improvement to its predecessors. Problem with the method arises when the analytical solution of the semi-discretized system is not available, which is the case for numerous problems. In the most recent attempt to solve the issue, a shooting method was proposed for elastostatic problems. Generality of the method removes any concerns regarding the type of governing equations since it no longer needs any analytical solutions. In this study, the method is further developed to deal with elastodynamic problems of viscoelastic media in the frequency domain, for which the closed-form solution is not available. Adopting the shooting method, the two-point boundary value problem of each subdomain is treated as a second-order initial value problem. Boundary conditions of the bounded subdomains are formulated by enforcing equilibrium at both ends. On the other hand, in contrast to linear elasticity, neither forces nor displacements vanish at infinity. As a result, a special treatment is required to deal with the boundary conditions of the unbounded subdomains. A Runge–Kutta–Nyström method, which consists of an embedded pair of adjacent order, is utilized to integrate the strong form of oscillatory equations enabling local error estimation and adaptive step-size control. This guarantees efficiency since the integration proceeds not by equal step-sizes, but by equal user-defined local errors. In the first step, analytical solution of a viscoelastic half-space subjected to a harmonic strip load is used for the verification process. First, the half-space is discretized by Voronoi cells and each truncated edge is defined using an unbounded subdomain. Next, one bounded subdomain is used to define the whole bounded area, and one unbounded subdomain resembles the radiation condition of the far-field boundaries. For the cases involving only bounded subdomains, three other numerical tests, including a perforated plate, an L-shaped panel, and a bi-material specimen are employed, and the effect of discretization method on the results is analyzed. The method is a huge step forward since the size of subdomains are not restricted, far-field boundaries can be arbitrary-shaped, hysteretic damping can be naturally included, no additional unknowns are introduced, no compound matrices are defined, no preconditioning matrices are needed, and a simple unified approach is used for both bounded and unbounded subdomains.

Predicting thermally induced edge-crack initiation using finite fracture mechanics

In temperature-loaded bi-material joints, highly localized stress concentrations occur at the bi-material junction at the free edge. This so-called free-edge effect may cause premature failure in form of an interface crack emanating from the free edge. In the present work, thermal crack initiation is investigated using a coupled stress and energy criterion within the framework of finite fracture mechanics by the example of a uniformly cooled epoxy–glass bi-material specimen. The mechanical analysis is based on the assumption of a plane-strain state, providing a simplified two-dimensional model. Interface stresses and the energy dissipation due to crack initiation are computed efficiently using the scaled boundary finite element method (SBFEM) and the effect of the layer thickness on crack initiation is studied. Dimensional analyses revealed that interface stresses and energy dissipation can be scaled to an arbitrary layer thickness such that only few model evaluations are required. For validation purposes, a finite element reference solution is provided and compared to the results obtained by the SBFEM approach. In addition, a cohesive zone model is applied to validate the predictions of the coupled stress and energy criterion.

Effect of salt spray ageing on the fracture of composite-to-metal bonded joints

Abstract This work investigates the effect of long-term environmental exposure on the performance of composite-to-metal bonded joints. Specimens are manufactured using a carbon-fiber reinforced polymer (CFRP) co-bonded to a steel member with epoxy adhesive and aged in a salt spray chamber. The mixed-mode fracture behavior of the non-aged and aged specimens is assessed using the mixed-mode bending (MMB) test apparatus. The fracture energy is calculated using the finite elements method and an analytical approach, the strain-based method (SBM). The SBM showed to be a simple and accurate method to obtain the total fracture energy and the fracture mode ratio of the bi-material specimen. Ageing increased the fracture toughness at crack initiation by 27% for specimens loaded at 20% mode II and 7% for specimens loaded at 15% mode II. This can be related to the shear behavior and plasticization of the adhesive material. During crack propagation, the fracture toughness remained similar for specimens loaded at 20% mode II and decreased by 15% in specimens loaded at 15% mode II. Fractography analysis together with chemical characterization showed that the penetration of moisture at the edges of the fracture surface produced adhesive failure in these regions affected by moisture. Moreover, the failure mode at the unaffected regions of the fracture surface shifted from cohesive to a combination of thin-layer cohesive and adhesive failure after ageing. The results contributed to describe the effect of ageing on the fracture behavior of bonded materials.

Determination of complex stress intensity factors for interface cracks in bi-material specimens subjected to ununiform stresses

This paper presents the calculation of complex stress intensity factors (K) for interface cracks in commonly used bi-material specimens subjected to arbitrary ununiform stress fields. First, detailed finite element analyses were carried out for cracks in centre-cracked plate (CCP) and single edge-cracked plate (SECP) bi-material specimens of different material combinations under non-uniform stress distributions. The complex SIFs were determined for the loading cases of uniform, linear, parabolic or cubic stress distributions applied to the crack faces in both normal and shear directions. Then, general mathematical forms of the two complex crack face weight functions for interface cracks, one for normal loading, and one for shear loading, have been formulated by taking advantages of the knowledge of specific analytical complex weight functions available in the literature, and certain properties of the complex weight functions in general. The existence of the general functional forms simplifies the determination of these weight functions for specific crack geometrical configurations and bi-material combinations. The determination of a specific weight function is thus reduced to the determination of the unknown parameters of the generalized weight function functional forms. It was demonstrated these unknown parameters can be determined from reference stress intensity factors. This method was used to derive the complex weight functions for interface cracks in bi-material CCP and SECP specimens. The derived closed-form weight functions were then validated against complex stress intensity factors solutions for several non-linear normal and shear stress distributions.

Design of auxetic plates with only one degree of freedom

A continuum elastic plate has infinite degrees of freedom: according to the applied loads, it assumes the shape that the minimization of the total energy prescribes, in dependence of the material it is made of. The possibility to control the shape of a morphing structure is receiving an increasing attention in several fields; in this connection, if a classical elastic plate is considered, it is not possible, in general, to tune the elastic properties of the material in order to select, between the infinite deformation modes the plate may have, the one desired. We present a prototypical case that tries to satisfy this desideratum, opening the way to the systematic design of microstructure’s geometries to fully control a system’s shape independently of the applied loads. A novel yet simple architecture for thin plates having only one degree of freedom is proposed. The plate is realized as a tessellation composed by rigid equal hexagonal tiles hinged to each other along the sides, and it can deform in just one way, that is, into a predetermined synclastic surface, whatever loads are applied to it. Such tessellated plate also has a remarkable auxetic behavior in bending, with the ratio between transverse and longitudinal curvatures in uniaxial bending reaching values larger than one. Modeling assumptions and analysis results, at both the discrete and the continuum level, are verified by tests carried out onto additively manufactured bi-material specimens, showing that it is possible to design the deformed configuration by controlling the hexagons’ geometry. The proposed architecture for realizing auxetic plates with only one degree of freedom is highly scalable and easily manufacturable, and it can find applications for auxetic scaffolds, prosthetic stress shields, energy harvesters, and wearable devices.

Large deformation in bi-material components by XIGA and coupled FE-IGA techniques

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems.

Study of the failure properties and tensile strength of rock-mortar interface transition zone using bi-material Brazilian discs

The interface transition zone (ITZ) between aggregate and mortar of concrete has a weak resistance to static or dynamic loading and failure usually starts from this zone. Therefore, it is essential to study the failure properties and tensile strength of ITZ of concrete under static and dynamic loading. Accordingly in this paper, bi-material specimens of rock-mortar Brazilian Disc were designed. Two types of rock granite and sandstone with smooth and rough surface were selected to prepare the bi-material Brazilian disc (BBD) specimens. Meanwhile, to compare the difference of failure properties with single material, the Brazilian disc (BD) specimen of single granite, sandstone and mortar were also prepared. The static and impact tests were conducted using the BBD and BD specimens, and a split Hopkinson pressure bar (SHPB) device was applied in the impact tests. Because of asymmetry stress distribution in the bi-material Brazilian disk, the tensile strength was determined by an experimental-numerical method. In addition, to simulate the failure process in ITZ, numerical models of the BD and BBD specimens embedded with cohesive elements using Python language were established. The results show that under static loading, the tensile strength of bi-material sandstone-mortar is less than that of both the single sandstone and mortar, while the tensile strength of granite-mortar is slightly lower than that of the mortar but much less than that of the granite. The tensile strength of bi-material with rough rock surface is generally higher than that with smooth rock surface. The dynamic tensile strength is more than 20 times the corresponding static tensile strength, and the dynamic tensile strength increases with loading rates.