A Dynamic Punch Method to Quantify the Dynamic Shear Strength of Brittle Solids
S. Huang, K. Xia ∗), F. Dai Department of Civil Engineering and Lassonde Institute, University of Toronto, Ontario M5S 1A4, Canada ABSTRACT: Shear strength is a basic material parameter of rocks. It plays a vital role in the applications field of mining engineering and geotechnical engineering. Although static standards for measuring static shear strength of rocks are available, the shear behavior of rocks under the dynamic loading it is not well understood. This paper presents a punch device loaded by split Hopkinson pressure bar system (SHPB) to determine the dynamic shear strength of rocks. Thin disc samples are used to minimize bending stresses. An isotropic and fine-grained sandstone is used to demonstrate the measurement principle. It is observed that the shear strength of rocks increases with the loading rate. This device is applicable to fine-grained rocks with intermediate hardness. Keywords: Dynamic shear strength; Punch shear test; SHPB INTRODUCTION Shear strength is one of the most important material parameter for brittle solids. There are several suggested methods for the quantification of this parameter for brittle solids such as rocks [1, 2] and ceramics [3], and ductile materials such as polymers [4]. There are usually two methods proposed to measure the static shear strength of brittle solids: direct shear-box test and punch shear test. As compared to the direct shear-box test, the punch shear test owns the merits of applicability for high strength solids, minimization of the bending stresses on the samples, and facilitation of the sample preparation [5, 6]. The early works of punch shear tests have been performed to measure shear strength of rock using simple punch apparatus with thin disc samples [5, 7, 8]. As shown in Fig. 1a, Mazanti and Sowers introduced a simple punch to simulate the punching of a hard rock layer into a soft or compressible layer with concentrated load [7]. They concluded that the punch test results were comparable to the shear strength with zero confinement (i.e., the apparent cohesion in the Mohr-Coulomb theory). To minimize the bending stress on the rock specimen during shear tests, Stacey [5] employed a simple punch shear apparatus (Fig. 1b), which is adaptable for traditional compression testing frames. The compressive load produces two parallel shear failure surfaces in the test sample. Later, a Block Punch Index (BPI) test was developed [9]. The BPI test apparatus was designed to be fit into the frame of point load testing device and the index value was calculated by dividing the maximum load on the punch by the shear failure area. Schrier then established empirical relationships between the uniaxial compressive strength (UCS) and BPI, and between the Brazilian tensile strength and BPI. He suggested that the BPI can be used to predict the UCS of rocks [9]. Ulusay and Gokceoglu investigated the size effect of the test sample and a size-corrected BPI was provided and related to UCS (UCS = 5.5 BPI) [10]. They suggested a slightly different formula to calculate BPI and concluded that this index can be used as an alternative input parameter for intact rock strength in rock mass classification. This method became one of the suggested methods by the International Society of Rock Mechanics (ISRM) [11]. It is noted that in various engineering applications, brittle solids may be subjected to dynamic loadings due to impacts or blasting. It is thus desirable to develop a method to quantify the dynamic shear strength of brittle solids. In the laboratory, the common tool to carry out dynamic test is the split Hopkinson pressure bar (SHPB) developed by Kolsky [12]. Although the straightforward application of this apparatus is the dynamic compressive tests, SHPB can be use to measure other properties with proper modification of the sample geometry and assembly [13, 14]. Indeed, there were a few attempts to measure the dynamic shear properties of ductile materials and structures using SHPB. Li et al. utilized SHPB with punch system to conduct the dynamic fiber debonding and push-out experiment on model single fiber composite systems [15]. Dynamic ∗
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T. Proulx (ed.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series 99, DOI 10.1007/978-1-4614-0216-9_22, © The Society for Experimental Mechanics, Inc. 2011
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punch tests were also used to investigate the mechanical properties of metals [16, 17]. Motivated by the needs from engineering applications and the existing studies, the objective of this paper is to develop a dynamic punch shear device to quantify the dynamic shear properties of brittles solids. Loading
a)
Punch head Sample
Holder
Loading
b)
Punch head Sample
Holder
Fig. 1. Schematics of punch shear devices used by: a) Mazanti and Sowers [7] and b) Stacey [5]. GENERIC TESTING PRINCIPLES A 25 mm diameter SHPB system is utilized to apply the dynamic load for punch shear tests (Fig. 2). The SHPB consists of a striker bar, an incident bar and a transmitted bar. The length of the striker bar is 200 mm. The incident bar is 1500 mm long and the strain gauge station is 787 mm from the specimen. The transmitted bar is 1000 mm long and the stain gauge station is 522 mm away from the specimen. The bars are made from Maraging steel, with a yielding strength of 2.5 GPa, density 8100 kg m-3, Young’s modulus 200 GPa and one dimensional stress wave velocity 4970 m/s. A gas gun lunches the striker bar to impact on the incident bar and generates an elastic compressive wave toward the sample. At the sample assembly, the incident wave will be separated into two waves: an elastic tensile wave reflected back into the incident bar and a compressive wave transmitted into the transmitted bar. The incident wave ε i , reflection wave ε r and transmitted wave ε t are measured by strain gauges mounted on the incident bar and the transmitter bar, respectively.
Strain gauge
Striker
Incident bar
Transmitted bar Sample
holder
Fig. 2. Schematics of Split Hopkinson Pressure Bar for dynamic punch shear tests. Using these three waves, the dynamic forces P1 and P2 on both ends (Fig. 3) of the sample assembly can be calculated [18]:
P1 (t ) = EA[ε i (t ) + ε r (t )] P2 (t ) = EAε t (t )
(1) (2)
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where E and A are Young’s modulus and cross-sectional area of the bars, respectively. Front cover
Rear supporter
P1 Incident bar
P2 Transmitted bar
Fig. 3. Schematics of the sample holder in SHPB. When the test is under dynamic force equilibrium condition (i.e. P1 = P2), the inertial effect in the dynamic test can be ignored [14, 19]. In this case, the punch shear stress in the sample can be calculated using the following equation:
τ=
P πDB
(3)
where τ is the punch shear stress; P = P1 = P2 is the loading force; D and B are the diameter of incident bar and the thickness of the disc specimen, respectively. It is noted here that we divide the load by the total shear area to obtain the shear stress, in a similar way to most other static punch shear studies. The maximum value of τ is considered as the punch shear strength τ 0 of the sample tested. A special holder is designed to support and protect the sample during dynamic punch tests. Conventional punch shear systems for static tests usually have two kinds of punch heads: cylindrical punch head and block punch head (Fig. 1). For dynamic punch tests using SHPB, an annular holder is usually adopted [15-17]. In this paper, the stainless steel holder consists of a front cover and a rear supporter, which are jointed by screw to hold the sample as shown in Fig. 3. The purpose of the front cover is to reduce the bending force during tests and additional damage on samples during and after the tests. The inner diameter of the rear supporter is 25.4 mm, 0.4 mm larger than the diameter of the incident bar to accommodate shear deformation. The incident bar serves as the punch head and the rear supporter is attached to the transmitted bar. The outer diameter of the entire holder is 57 mm. APPLICATIONS TO LONGYOU SANDSTONE Sample preparation
Fig. 4. a) Typical virgin and tested samples; b) The rock ring and rock plug produced in a typical dynamic punch shear test (the unit in the picture is centimeter).
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In this study, Longyou sandstone (LS) from Zhejiang Province of China is chosen to demonstrate the feasibility of the proposed dynamic punch device. LS is a fine-grained homogeneous sandstone, with negligible clay content (Fig. 4a). The mineral composition of the rock has been reported by Huang et al. [20]. The porosity of LS is measured as 17%, the density 2150 kg/m3, and the P-wave velocity 1600 m/s. The sample for the punch test is first drilled into 44 mm in diameter cores. These cores are then sliced to discs with nominal thickness of 16 mm and further polished into 14 mm thick thin discs. Dynamic force balance In traditional SHPB tests, the mismatch between forces added on both end of sample leads to the so-called axial inertia effect [21]. This problem can be overcame by using the pulse shaping technique, which is especially useful for investigating the dynamic response of brittle materials [13, 22]. In this work, the C1100 copper disc is used as the shaper material. During tests, the striker impacts on the pulse shaper before the incident bar, generating a non-dispersive ramp pulse propagating into the incident bar and thus facilitating the dynamic force balance of the specimen.
80
In Re In+Re (P1)
60
Force (kN)
40
Tr (P2)
20 0 -20 -40 -60 -80 0
50
100
150
200
250
300
Time (μs)
Fig. 5. Dynamic force balance check for a typical dynamic punch test with pulse shaping Fig. 5 shows the forces on both ends of the sample in a typical test. From Eq. (1) and Eq. (2), the dynamic force P1 is proportional to the sum of the incident (In) and reflected (Re) stress waves, and the dynamic force on the other side P2 is proportional to the transmitted (Tr). It can be seen from Fig. 5 that the dynamic forces on both sides of the specimens are almost identical during the entire dynamic loading period. The inertial effects are thus eliminated because there is no global force difference in the specimen to induce inertial force. Thus the static shear strength formula Eq. (3) can be utilized to analyze the dynamic results. Determination of the loading rate The dynamic strength of brittle solids exhibits the rate dependence [13, 23]. The loading rate for punch shear is characterized by τ& obtained from the time evolution of the shear stress. Fig. 6 shows dynamic loading history for a typical shear punch test. There exits a regime of approximately linear variation of shear stress from 50 µs to 85 µs. The slope of this region is determined from a least squares fit, shown as a line in the figure and this slope is used as the shear loading rate for the dynamic test.
161 25
Stress (MPa)
20
15
10
5
.
τ=440 GPa/s
0 0
30
60
90
120
150
Time (μs)
Fig. 6. Typical shear stress-time curve for determining the loading rate. Experimental results The thin disc sample is punched into a rock ring and a rock plug as shown in Fig. 6b. Few visible radial cracks can be identified on the ring. To recover the plug, a momentum-trap technique is utilized in this study. The momentum-trap technique proposed by Song and Chen [24] is adopted in this work. The working principle of this technique was presented elsewhere [25]. The main idea of using this method here is to constrain the displacement of the incident bar and thus to protect the plug from multiple loading. The soft-recovery of the rock ring and rock plug is thus possible as shown in Fig. 6b. The shear stress – shear displacement curve for a typical test is shown in Fig. 7. It can be seen that the shear strength is achieve at the displacement of 0.12 mm. We used displacement here to be consistent with the suggested direct shear and torsional shear methods by ISRM [1]. 25
Stress (MPa)
20
15
10
5
0 0.00
0.05
0.10
0.15
0.20
0.25
Displacement (mm)
Fig. 7. Shear stress vs. displacement for a typical test. Dynamic punch shear experiments were conducted under different loading rates to investigate the rate effect for LS. The dynamic punch shear strengths were obtained at loading rates ranged from 566 GPa/s to 1800 GPa/s. The maximum dynamic strength is 36.8 MPa. For reference the static punch shear strength is measured as 11 MPa for this rock. The static test was performed on Material Test System with 0.001 mm/s loading speed. The variation in flexural tensile strength as a function of loading rate is illustrated in Fig 8. It is evident from Fig.8 that the strengths of LS with the loading rates in the loading. The punch shear strength of LS is thus strongly rate dependent.
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Punch Shear Strength (MPa)
40
30
20
10 0
500
1000
1500
2000
Loading Rate (GPa/s)
Fig. 8. Punch shear strength of LS and test loading rate. CONCLUSION A dynamic punch shear method has been developed in this work to quantify the dynamic shear strength of brittle solids. The dynamic load was applied by a split Hopkinson pressure bar (SHPB) system, and the pulse-shaping technique was adopted to achieve the dynamic force balance and thus eliminate the axial inertial effect. A special sample holder was designed to protect the sample and in combination with the momentum-trap technique, it enabled soft-recovery the ring and plug produced by the punch. This dynamic punch method was applied to Longyou sandstone (LS). This dynamic punch shear method can be readily applied to various brittle solids in addition to the sandstone used in this work. ACKNOWLEDGEMENTS This wok was financially supported by the CAS/SAFEA International Partnership Program for Creative Research Teams (No. KZCX2-YW-T12). S.H. and K.X. acknowledge the support by NSERC/Discovery Grant No.72031326. REFERENCE [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8]. [9].
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