THEORETICAL & APPLIED MECHANICS LETTERS 1, 051002 (2011)
Quasi-static tensile deformation and fracture behavior of a highly particle-filled composite using digital image correlation method Zhongbin Zhou, Pengwan Chen,a) Baoqiao Guo, Zhuoping Duan, and Fenglei Huang State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
(Received 01 August 2011; accepted 12 August 2011; published online 10 September 2011) Abstract Polymer bonded explosives (PBXs) are highly particle-filled composite materials. This paper experimentally studies the tensile deformation and fracture behavior of a PBX simulation by using the semi-circular bending (SCB) test. The deformation and fracture process of a pre-notched SCB sample with a random speckle pattern is recorded by a charge coupled device camera. The displacement and strain fields on the observed surface during the loading process are obtained by using the digital image correlation method. The crack opening displacement is calculated from the displacement fields, the initiation and propagation of the crack are analyzed. In addition, the damage evolution and fracture mechanisms of the SCB sample are analyzed according to the strain fields and c 2011 The Chinese Society of Theoretical the correlation coefficient fields at different loading steps. and Applied Mechanics. [doi:10.1063/2.1105102] Keywords highly particle-filled composite, digital image correlation, deformation and fracture, damage evolution Polymer bonded explosive (PBX) is a highly filled composite material of crystalline explosives (90%–95% by weight) in a few percent polymer binder. The PBX is a kind of functionally energetic materials widely used as energetic fillings in both civil and military applications. As brittle material, initial defects exist in PBX. New defects will also occur and grow when PBX subjects to loads. These cause the damage in PBX material. Damage in PBX not only degrades the mechanical property, but also greatly affects the combustion and detonation ability of the material. The mechanical properties of PBX subjected to a range of conditions are important criteria to determine the safe working life. Therefore, determination of the fracture deformation and failure strength,1–4 and the influence of strain rates and temperatures on the mechanical properties5,6 of PBX, have drawn great interest of many researchers. From the existing literatures, there are many techniques to quantify the deformation of bodies under stress. The strain gauge and extensometer are common techniques which can provide strain from the uniform deformation information. But they are unable to provide data on microstructural deformation. Significantly, the strain gauge measures the deformation at a single point, and the gauge on the sample surface may provide local reinforcement. However, the optical techniques, on the other hand, show the advantages that they can measure the whole deformation field without contact, and it is suitable to measure the whole strain fields until failure. Recently, they were successfully used in displacement and strain field measurement of PBX. Many beneficial works were reported from Cavendish Lab.7 The quasi-static deformation and fracture have been studied by moir´e technique.8 Rae et al.9,10 used a) Corresponding
author. Email:
[email protected].
the digital image correlation (DIC) method to study the effect of thermal aging on the UK PBX. The microscopic mechanical response of PBX was studied by DIC.11–13 Moreover, the DIC was used to study the fracture behavior of PBX at high-strain-rate.14,15 It is reported that the initiation and propagation of cracks are the dominant mechanical failure mechanism of high explosives, and the crack could affect both the safety and detonation performance of weapons and munitions systems. However, cracks are hard to observe until they grow large enough. Using the DIC technique, we can determine the initiation and propagation route of cracks.12 In addition, by analyzing the strain fields during deformation, it can be concluded that the heterogeneity of strain field can be characterized as a damage factor. The damage evolution of the material can be obtained by calculating the standard deviation of every strain field during loading. Therefore, in this paper, a semi-circular shaped sample was loaded quasi-statically. The tensile deformation and fracture behavior of the sample was studied by using DIC technique. In addition, the crack opening was determined, the initiation and propagation route of cracks was quantitatively measured, and the damage evolution in the sample during deformation was studied. A PBX simulation material was used in this work, which comprised inorganic particles held together by a fluoro-rubber. The samples are produced in a steel pressing mold by hot pressing. The pressing pressure is 200 MPa, the temperature is 100 ◦ C and the duration of pressing is about 1 h, then a disc shaped sample is obtained with diameter of 20 mm and thickness of 10 mm. It was symmetrically cut into two slices; therefore, semicircular shaped sample was obtained. Figure 1 shows the geometry of semi-circular bending (SCB) test. The SCB sample was pre-notched with a 0.2 mm thickness steel blade and subjected to a three-point bending load.
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Fig. 1. The SCB test.
The initial pre-notch, which is about 1 mm length, was cut along the line of symmetry at the sample edge and oriented along the compression direction. The DIC technique is a rapidly developing technique in experimental mechanics.16,17 Recently, it was used widely to measure the deformation field at macro and micro-scale. A random speckle pattern was obtained by spraying paints on the sample surface (as shown in Fig. 2). In the testing, the images of speckle pattern were recorded by using a charge coupled device camera at a framing rate of 5 frames per second, with a high resolution of 1 624 pixel × 1 236 pixel in each image. A sub-image with resolution of 29 pixel × 29 pixel and step size of 5 pixel was used in DIC analysis. By correlation matching the same zone of the two speckle images before and after a deformation, the full-fields of displacement and strain were obtained. The criterion for matching two images is given by using the correlation coefficient c, which is given by18 f (x, y) · g(x∗, y∗) , (1) c = 1 − f 2 (x, y) · g 2 (x∗, y∗) where (x, y) and (x∗ , y ∗ ) are Cartesian coordinates of a material point in the image of the undeformed and deformed patterns, respectively. The f (x, y) and g(x∗ , y ∗ ) are light intensities at the point in the corresponding images. The correlation value c varies from 0 to 1, with 0 signifying a perfect match between the two images. In DIC analysis, the area of interest was chosen for the displacement and strain fields measurement. In order to determine the crack opening displacement, we picked up two points (as shown in Fig. 2, labeled ‘A’ and ‘B’) symmetrically in the front of the crack tip, which is perpendicular to the orientation of the crack. With the increase of external force, the specimen deformed continuously. After the peak load (Pm in Fig. 3), the crack will initiate; therefore, the distance between these two key points can be determined by δ = δB −δA , which represents the opening displacement of the crack. Figure 3 shows the variation of the crack opening displacements and external loads as a function of loading times. An obvious feature of such a variation is that crack opening exhibits a sharp transition during the process of the deformation. It is seen that during the early stage of the deformation, crack opening δ = 0 and changes very
Fig. 2. Determination of crack opening displacement.
Fig. 3. External load curve and crack opening displacement curve versus loading time.
little. After a particular moment of time, δ monotonically increases with the increase of the loading time, and at this moment, the external load reaches its peak load. After this, the load rapidly decreases. In the DIC calculation, the correlation coefficient c is a function of the two random speckle images before and after deformation. When the two small images match each other, the correlation coefficient reaches a minimum. However, when damage or cracks develop in the small region during deformation, the value of the coefficient c becomes bigger than other regions where no damage or cracks are presented. In this work, based on the above discussion, we use the correlation coefficient to quantify the location and extent of cracks in SCB specimen. Figure 4 shows the contour plot of normalized correlation coefficient at four loading states. For PBX specimen, at moment (a), the normalized correlation coefficient over the entire specimen surface is a constant, the magnitude of coefficient c approximates to 0, indicating that the two speckle images match each other very well, no damage is formed. In the subsequent moments, (b), (c) and (d), in some regions within the specimen surface the normalized correlation coefficient becomes bigger than other regions. In moment (b), the small
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Theor. Appl. Mech. Lett. 1, 051002 (2011)
Fig. 5. Strain (εx ) fields of SCB sample under different loading steps.
5(c). It is believed that during this process the initial damages underneath the specimen surface may be activated and some new damages will generate. Results indicate that a possible fracture path will follow the concentrated strain band and the specimen will break into two parts eventually under tensile stress action. Fig. 4. Correlation coefficient fields under 4 different loading steps in SCB test.
cracked region formed around the preset crack, and at the next moments (c) and (d), the cracked region grows larger. Specially, at moment (d), a single dominant crack is generated along the orientation of preset crack. Figure 5 shows the strain field plots at three loading steps of P = 320 N, P = 340 N and P = 290 N respectively. In Fig. 5(a), it can be noted that a concentrated tensile strain band localizes in the vicinity of tip of the prefabricated notch. Meanwhile, it can also be noted that a localized strain presents in an area near the anvil, which is caused by the point-contact between anvil and specimen. As external force applied further, the localized strain band evolves continuously along the pre-notch orientation, this is displayed in Figs. 5(b) and
In this work, the SCB test was used to study the tensile deformation and fracture behavior of a simulant PBX. Based on DIC technique, the full-fields of displacement and strain were measured. The crack opening displacement was determined, and the initiation and propagation route of the crack were quantitatively studied. In addition, the damage evolution of the SCB sample was determined based on tensile strain fields. The results indicate fracture mechanisms of the sample, showing that the SCB sample fractured under extension stress action with a split failure. This work was supported by the National Natural Science Foundation of China (10832003), the National Basic Research Program of China (613830202), the NSAF (11076032). The authors thank Prof. Nie Fude of Institute of Chemical Materials, Chinese Physical Academy for providing PBX mock materials.
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