Optimizing the Shape and Size of Cruciform Specimens used for Biaxial Tensile Test

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1 Applied Mechanics and Materials Vol. 658 (2014) pp Submitted: (2014) Trans Tech Publications, Switzerland Revised: doi: / Accepted: Optimizing the Shape and Size of Cruciform Specimens used for Biaxial Tensile Test ANDRUSCA Liviu 1,a *, GOANTA Viorel 1,b and BARSANESCU Paul Doru 1,c 1 Gheorghe Asachi Technical University of Iasi, Department of Mechanical Engineering, Mechatronics and Robotics, Bvd Prof. Dr. doc. Dimitrie Mangeron, 67, Iasi, Romania a * sir_liviu@yahoo.com, b goantav@yahoo.com, c paulbarsanescu@yahoo.com Keywords: cruciform specimens, biaxial tensile test, stress state, finite element analysis. Abstract. Testing cruciform specimens subjected to biaxial tension is one of the most widely used experimental techniques and more accurate at this time to determine the mechanical properties of materials and to verify the failure theories. This type of experiment allows the continuous monitoring of behavior of materials from the beginning of deformation until fracture under different ratios of forces and directions of the deformation, which transforms it into a very versatile testing method. We have varied the number of parameters and their values in order to achieve a uniform distribution of biaxial state of stresses and strains in the area tested. In theory, any material can be tested by stretching a biaxial cruciform specimen, but must be investigated in what way the shape of the specimen influence the data obtained. In this paper are presented the requirements that must be fulfilled by the samples used for tensile / compression biaxial tests and the design of cruciform specimens through FEA that meet these demands. Introduction Utilization of materials in a very wide range of applications has led to the need to investigate in detail their behavior for different stress states. Research on the behavior of materials subjected to multiaxial loadings are closely related to areas such as physics, chemistry, mathematics and computer science and seeks to generate ideas, methods and concepts to provide precise answers to industrial and scientific problems and challenges. Knowing and understanding behavior of materials in plane and spatial stress state is essential in design of machine elements and structural elements. For this purpose is necessary to develop test methods for applying complex multiaxial loadings [1]. A first step towards in this sense is the biaxial tensile testing, in plane, on orthogonal directions, of cruciform specimens, that is the more accurate method to obtain a uniform biaxial stress state [2, 3]. Cruciform specimens can be used for in plane biaxial fracture, deformation and fatigue tests [4-8]. Along the time there have been proposed and tested different types of samples designed to achieve biaxial stress state (thin tubes subjected to pressure and traction, plates subjected to double bending, token type discs subjected to compression, etc.), however the best results were obtained using cruciform test specimens subjected to tensile or compressive tensions. The efforts made by many researchers in the last decades to develop experimental procedures for biaxial tensile / compressive tests have been hampered by the complexity of necessary elements: a versatile testing machine, optimal design of a cruciform test specimen and, not least, a precise measurement system. In order to provide more useful data, cruciform specimens must satisfy a set of requirements: possibility to align (center) the cruciform specimen in test system; generation of homogeneous fields of biaxial stresses and strains in central part, large enough, so failure occur in the gage section; localization of yielding in the central area; possibility to observe evolution of stress state after yielding initiation; to accept ratios of arbitrary biaxial loading, in order to generate an envelope of failure; values of stresses in the region tested to be comparable to the nominal values obtained by dividing forces applied to the transverse area, etc. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, (ID: , Technical University Gh. Asachi from Iasi, Iasi, Romania-24/09/14,07:58:05)

2 168 Advanced Concepts in Mechanical Engineering I Design of cruciform specimens This study is intended to evaluate the factors that might influence the failure mode of the specimen and distribution of plane stress state in the central part. The magnitude and number of cruciform specimen geometric parameters varies depending by the type of material of which it is made and the shape and size of them. The size of arms width depends on the capacity of test machine. Choosing the thickness of cruciform specimen depends on the material and must allow a plane state stress in the region of interest. The objectives to be reached by the optimization procedure of the cruciform specimen are as follows: maximizing the surface region of uniform biaxial stress in the center specimen, the maximum value of stress is attainment in gage section, minimizing shear stresses in central zone, minimizing the influence of stress concentrators outside the tested region and originally flow appear in the middle of the specimen. Meeting simultaneous of all these requirements is, however, a very difficult task. Cruciform specimen design optimization involves two major aspects: type of material used and geometrical configuration. (a) (b) (c) Fig. 1 Evolution of cruciform specimen types Figure 1 shows the evolution of configuration cruciform specimens: basic idea behind of the design of biaxial tested specimen was adding a second direction perpendicular to the specimen used in uniaxial testing (Fig 1.a). To improve the biaxial stress state from the middle of the specimen was proceeded to a thickness reduction, the cutting up having various forms (Fig 1.b presents one of them). Due to the development of testing procedures of biaxial cruciform specimen, has been developed a new version, by adding grooves in the arms of the specimen, which causes a more uniform biaxial stress state with maximum values at the center (Fig 1.c). By effectively combining three factors: geometrical shape, thickness reduction and introduction of the grooves can be obtained an optimal cruciform specimen. The big challenge in designing cruciform specimens is determining an efficient combination of variables (geometrical and technological) that satisfies the conditions above. To focus a uniform state of stresses and strains and their maximum values to be in the center of the specimen (gage section), have been proposed several solutions: directly (reducing the thickness of the central region and strengthening the region of arms) and indirectly (heating the test zone). Cruciform specimen design includes several phases: determination of stress state in test specimen through FEA; determination of equivalent stresses using a limit state theory. Von Mises theory is successfully used in case of isotropic materials, with predominantly ductile behavior.it requires the use of only one parameter, obtained through uniaxial testing; comparing the calculated stresses with the value of uniaxial tensile yield point. The measurement of deformations in cruciform specimen during biaxial tests is essential because stresses cannot be calculated with simple formulas, as in the case of uniaxial testing. Systems for measuring displacements and strains can be divided into two large categories: with measurement of local field, using for example electrical strain gauges;

3 Applied Mechanics and Materials Vol with measurement of global field, using for example optical methods like digital image correlation (DIC). If there is no good agreement between the experimental stresses and stresses provided by FEA, design process you will be restarted. Until this time has not been established any international standardized procedures for the shape and size of cruciform specimen subjected to in plane biaxial tension / compression tests. Biaxial experiments are performed by means of two types of machines - standalone and dispositives attached to the universal testing machine. Geometric parameters of cruciform specimen Specimen parameters in this study were: W - arms width, L1 - specimen overall length, L2 - clamping region length, L3 - arms length with constant thickness, L4 - central area length with constant thickness, R1 region radius of reduced thickness, R2 region radius of intermediate thickness, R3 - region radius with full thickness, R4, 5 radius between the two areas with different thickness, T1- arms thickness, T2- central area thickness. (b) (a) Fig. 2 Cruciform specimen parameters: a) 2D CAD view; b) FEA model 3D c) detail view of transition zone between central thickness and arms thickness Values for 1/8 of the whole specimen are shown in table 1. Table 1 Values of parameters for geometry type 3 Parameters L1 W L2 L3 L4 R1 R2 R3 R4 R5 T1 T2 Values [mm] Two of the major problems found in the case of cruciform specimen are: the presence of stress concentrators in intersection zone of arms (shown in Figure 2.b - zone A), due to the way how the connection is made (corner region, shown in Figure 2.b - zone B ) and in transition zone between the two thicknesses, from the central part (shown in Figure 2.b - (c)

4 170 Advanced Concepts in Mechanical Engineering I zone C); (represented in fig.2.c - zone I, is region of central reduced thickness, zone II is transition zone between central thickness area and arms thickness area and zone III, that is region of arms thickness); method of calculate the stresses from the forces acting on the central section whose area is varies during experiments. Finite element modelling The concept of a multiaxial testing system capable of producing input data in constitutive relations for a particular type of material creates the perspective of reducing the number of tests performed, increasing the quality of the experiments and getting fast results that can be used later in the design process. To simulate the behavior of the material is very important that the model (geometry, dimensions and material characteristics) to be as detailed well as precise as results obtained to be those desired. Therefore, it is intended that for materials with brittle preponderantly behavior, failure to start from the central area as a result of the action of normal stresses, and to propagate in a direction at 45 degrees with respect to loading direction. For materials with ductile preponderantly behavior, failure is initiated by the action of shear stresses. Due to symmetry, finite element analysis was used only 1/8 of the total specimen, this rule applying for load conditions and for boundary conditions. The magnitude for applied pressure to the specimen arms surface was 100 [N/mm 2 ]. Assumptions for FEA were those of elasticity theory. The material adopted to perform finite element analysis was aluminum alloy 6061 T4, that be used in the experimental tests. Simulation was carried out using Algor program, analysis being of the type "Static Stress with Linear Material Models". Elements type was "brick", considering that the material has an isotropic behavior regarding how it will deform. FEA were conducted on several versions of cruciform specimen shapes and sizes. In Figures 3 and 4 are showed normal stress arrangements and shear stress distributions just for three more representative types of geometries, each representing a class of analysis. (a) (b) (c) Fig. 3 Von Mises stresses distribution: a) geometry type 1, b) geometry type 2; c) geometry type 3 (a) (b) (c) Fig. 4 Shear stresses distribution: a) geometry type 1, b) geometry type 2; c) geometry type 3

5 Applied Mechanics and Materials Vol Results and discussion The ratio of stress values registered on the distance between the middle part and the edge of the specimen corner, on the direction at 45 degrees, is the coefficient used to describe the differences between the three types of geometries chosen for comparative study from this paper. FEA was started from three kinds of test specimens with different overall dimensions For each of them has been studied the influence of the shape of arms intersection and connecting radius of the thickness transition zone between the central part and arms region. The ratio between the arms region thickness and central region thickness was constant, for the three types of geometries. Examination of geometrical parameters used in the optimization process was performed as follows: was submitted an analysis for a first type of geometry, with the intersection of the arms (corner region) as a right angle, with a small fillet radius; stress state was monitored during analysis and noticed that it is uniform and maximum values of the stresses are concentrated in gage section, but the presence of stress concentrators in the outer central area is very significant, which may influence the failure mode of the specimen (rupture can possibly produce in the arms specimen); to minimize the influence of stress concentrators outside the central area, was proceeded to modification of the corner shape, by changing the shape through a circular arc that have starting points in the region of arms clip ends; this led to a uniform state of stress in the area tested, to the increase of their maximum values and forming of a gradient in the direction of 45 (distance between point 1 and point 2). Appearance of high levels of stresses in the corner vicinity, on the direction to 45 degrees, it may cause failure otherwise than the one desired (failure by crack propagation to 45 degrees, starting from the middle); in the case of geometry type 3, for the construction of arms intersection shape was used a spline type curve (drawn by three points 2,3 and 4 - Figure 2a), resulting the smallest distance between the middle and corner (distance between point 1 and point 2 - Figure 2a) If the forces acting on the two perpendicular axes are equal during the entire period test, shape of arms intersection area generates different maximum values the stresses in the two regions of interest: center of the specimen, respectively specimen corner. (a) (b) Fig. 5 Graphic representation of the gradient (direction of evolution) at 45 for the three geometries: a) von Mises stresses; b) shear stresses

6 172 Advanced Concepts in Mechanical Engineering I The value of shear stresses is maximum in corner specimen in each of the three cases analyzed. Initiation of crack propagation on the materials with ductile predominantly behavior occurs in the corner of the specimen, because there can be found the maximum shear stresses. In the materials with brittle preponderantly behavior crack initiation, in region with uniform biaxial stress state where normal stresses have maximum values. Factors that significantly influence the nature of failure mode of materials (ductile or brittle), at a time, are: temperature, type of loading (simple or composed requests, static or dynamic) and loading speed. Conclusions Cruciform specimen geometry optimization was performed in several successive stages: i) initial phase, in which the stress state was recorded for a first geometry studied, followed by ii) intermediate stage, in which different geometrical parameters were modified and the distribution of stress state was evaluated and completed with iii) final stage, in which the results are improved and objectives were accomplished. With the defined cruciform specimen configuration from FEA, and subsequently tests will be conducted. Through FEA a study was made which leaded to cruciform specimen geometry that meets the requirements initial, version with the best results being specimen what has a shape made by a spline type curve at the intersection of the arms. During the investigations has been pursued changes of geometrical parameters in order to minimize, possibly eliminate, inconveniences occurred during simulations. We can deduct two main ideas after this analysis: 1) uniform biaxial stress state and the maximum value of stresses are focused in the center of the specimen and 2) existence of a gradient in the direction of 45 degrees, this resulting from cruciform specimen geometry and not from the type of the material it is fabricated. Procedures with multidisciplinary approach which uses elements from static testing of materials, optimization techniques, techniques for measuring deformations and finite element modeling to identify material parameters may allow getting remarkable results. FEA will be followed by its manufacturing and it s testing in order to confirm the results of preliminary numerical study of geometrical parameters optimized values. References [1] M.C. Serna Moreno, J.J. López Cela, Failure strain and stress fields of a chopped glassreinforced polyester under biaxial loading, Composite Structures 103 (2013) [2] Escarpita et al., Biaxial tensile strength characterization of textile composite Materials, Instituto Tecnologico y de Estudios Superiores de Monterey, Monterey, Mexico [3] A. Hannon, P. Tiernan, A review of planar biaxial tensile test systems for sheet metal, Journal of Materials Processing Technology, 198 (2008) [4] F. Abu-Farha, L.G. Hector Jr., M. Khraisheh, Cruciform-shaped specimens for elevated temperature biaxial testing of lightweight materials, JOM, 61 (2001) [5] A. Makris, T. Vandenbergh, C. Ramault, D. van Hemelrijck, E. Lamkanfi, W. van Paepegem, Shape optimisation of a biaxially loaded cruciform specimen, Polymer Testing, 29 (2010) [6] A.M. Abdelhay, O.M. Dawood, A. Bassuni, E.A. Elhalawany, M.A. Mustafa, A newly developed cruciform specimens geometry for biaxial stress evaluation using NDE. 13th Int. Conf., Cairo, Egypt, May 26 28, [7] R.A. Cláudio, M. Freitas, L. Reis, B. Li, I Guelho, An optimized biaxial cruciform specimen for low capacity testing machines, 10th Int. Conf. on Multiaxial Fatigue and Fracture, Japan, [8] Y. Ohtake, S. Rokugawa, H. Masumoto, Geometry determination of cruciform type specimen and biaxial tensile test of C/C composites, Key Engineering Materials, 3 (1999)