Ghostscript wrapper for D:\Digitalizacja\MTS85_t23z1_4_PDF_artyku³y\mts85_t23z3_4.pdf MECHANIKA TEORETYCZNA 1 STOSOWANA 3 . 4 , 23 (1985) SHEAR TESTING OF COMPOSITES R. PRABHAKARAN Old Dominion University • • .; '.": Norfolk, Virginia 23S08, USA. • • : - . , -.., ;- .,, • Introduction Modern composite materials, incorporating fibers of glass, graphite, boron, etc., in a polymeric or metallic matrix, are finding increasing applications especially where high strengtli-to-weight and stiffness-to-weight ratios are required. The elastic constants and the strengths of composite materials have to be determined for designing structures utilizing these materials. For an orthotropic composite, there are five in-plane elastic constants and five values of strength that need to be determined. Referring to the in-plane material symmetry axes L and T, the elastic constants are the two Young's moduli EL, ET, the shear modulus GLr and the Poisson's ratios vLT and vTL. The strength properties are the tensile strengths SuSTt, the compressive strengths 5 t c , STc and the shear strength SLT. The stiffness and strength properties, of orthotropic composites along the material symmetry,axes can easily be measured using standard tension or compression specimens. While the procedure is very similar to that of measuring the stiffness and strength of a metal, the following precautions must be observed: (1) The electrical resistance foil strain gage should be large enough to cover several fibers and thus indicate the over-all response of the composite; (2) As the composite can be highly orthotropic, the gages must be aligned very accurately, in order to minimize misalignment errors; (3) While the transverse sensiti- vity of the strain gages is usually small, sometimes it must be corrected for, as in the measu- rement of vTL. . ,.; The determination of the shear properties of composite materials has proved to be much more difficult than that of longitudinal and transverse properties. So many methods and variations of each method have been developed that there is now much confusion as to which technique is applicable in a specific application. In this paper, some of the more widely used methods are briefly described and the Iosipescu shear test is considered in detail. Shear Testing of Composites An ideal test method must satisfy all or most of the following requirements: (1) The method must be simple and should not require special equipment; (2) The method should use small specimens with simple geometry; (3) The test results should be reproducible; 608 R. PRABHAKARAN (4) The data reduction procedure must be simple; (5) A uniform shear stress state accom- panied by negligible normal stresses must be produced in the test section. . The block shear test was originally developed for wood and it was applied to glass fiber reinforced composites in the 1950's. In order to overcome the difficulty due to the overturning moment, the symmetric block shear test was developed. But in both versions of the test, a state of pure shear is not produced. Stress concentrations are also present. In the mid-1960's, when the use of composite materials was rapidly increasing, the short beam shear test was developed for quality control. The test is simple but the shear stress is non-uniform and is accompanied by significant normal stresses. Crushing at the loading and support points is also a problem. The torsional shear of a circular thin-walled tube is the ideal test method to determine the shear modulus and the shear strength of any material. But from the practical point of view there are problems: (1) The cost of composite tubular specimens is very high; (2) The test apparatus tends to become more complex than at first it appears because bending must be avoided and the tube must be free to move axially; (3) Precautions must be taken to avoid crushing the regions where torques are. introduced and also buckling. The rail shear test is one of the more popular methods and it provides a good measure- ment for the shear modulus. In this method, a composite specimen is gripped along each side of a long narrow central region and the grips are loaded, in opposite directions. The central region is assumed to be in pure shear, But the grips introduce normal stresses [1]. The picture-frame shear test is also commonly used. In this test, a uniaxial tensile or compressive load is applied at two diagonally opposite corners of a rigid frame which is attached to the edges of a composite plate specimen. The biaxial picture-frame test, in which equal tensile and compressive forces are simultaneously applied along the frame diagonals, provides a more uniform shear stress in the specimen. But both versions require expensive test fixtures and significant amounts of test material. The off-axis tensile test utilizes a tensile specimen with the reinforcement oriented at a suitable angle to the specimen axis. An angle of 10 degrees has been strongly recommen- ded [2]. While this test has the merit of being very simple, care must be taken in machining the specimen and in mounting the strain gages as small misalignments can lead to very large errors. Unlike'conventional tensile tests, a large aspect ratio is required. A ratio of fifteen or greater has been suggested. Due to the presence of the normal stresses, this test gives the shear modulus and not the shear strength. The slotted-tension shear test is based on the principle that a uniform shear stress exists in a region if equal orthogonal tensile and compressive stresses are imposed on the element's edges. Planes of pure shear will exist at 45 degrees to the load axes. A slotted tensile specimen has been suggested [3]; the slots machined parallel to the longitudinal axis of the specimen ensure that the transverse compressive stresses are transmitted only to the test section. This shear test provides both the shear modulus and shear strength. The major disadvantage of this method is the complexity of the test apparatus which must ensure that the two orthogonal stresses must be equal at all times. The losipescu shear test and one of its modifications are described in the following sections. SHEAR TESTING OF COMPOSITES losipesca Shear Test 609 The Iosipescu shear test was originally developed [4] in the 1960's for determining the shear properties of metals and has recently been adapted for composite materials. In an isotropic material, the Iosipescu shear test induces a state of pure shear at the specimen mid-section by applying two counteracting moments. Ninety-degree notches are machined in the specimen, as shown in Fig. 1. The parabolic shear stress distribution found in beams of constant cross-section is changed to a constant shear stress distribution in the region between the notches. As shown in Fig. 2, the specimen midsection (between the notches) is free of any bending stress. Fig. 1. Iosipescu shear specimen a-b -*—'—- a-b i V • /s i£s_ : ; la-b I 1 • 1 j **,—-,—u—t. load Diagram a-b ' Pb n-b . . . Shear Diagram Pb a-b Pb/2 Moment Diagram • • •• Fig. 2. Loading, shear and moment diagrams for Iosipescu specimen 17 Mech. Teoret. i Stos. 3-4/85 (510 R. PBABHAKARAN An extensive finite element analysis of the Iosipescu specimen has been performed [5], It has been shown that while the longitudinal stress due to bending is small over the test section, significant transverse compressive stresses are present due to the applied loads. The normalized reaction force profile for the upper loading point [5] is shown in Fig. 3, The compressive stresses rise rapidly towards the edge of the notch and the influence of these loading-induced compressive stresses extends into the test section of the specimen. 0.0 • B -0.5 0.0 Normalized distance from cenlerline Fig. 3. Normalized compressive force distribution for Iosipescu specimen This indicates that the loading surfaces need to be shifted away from the notches in the specimen. Normalized shear stress contours indicate a shear stress concentration factor of 1.3 for isotropic materials and a shear stress concentration factor of 2.0 for orthotropic ma- terials with an orthotropy ratio of 13. These results show that the notch geometry needs to be modified in order to minimize the shear stress concentration. In reference [5], the effect of notch depth, notch angle and notch tip radius on the1 shear stress concentration has been studied by finite elements. The notch depth does not appear to have any significant influence. In the case of isotropic as well as orthotropic materials, as the notch angle is increased from 90° to 120°, the shear stress concentration decreases while the average shear stress across the test section tends t o be more uniform. The notch tip radius has a very similar influence. From a sharp notch, as the radius at the notch tip is increased to 0.100 in., the shear stress distribution becomes more uniform and the shear stress concentration drops, especially for materials with a high degree of orthotropy. Asymmetrical Four Point Bend Shew Test This test is an outgrowth of the Iosipescu shear test and the specimen mid-section is again subjected to a shear force without an accompanying bending moment [6]. The test, as shown in Fig. 4, applies concentrated forces to the specimen through cylindrical rods which can cause local crushing on the edges of the specimen. Doublers must be glued on to the faces of the specimen to prevent this crushing. The specimen need not be machined to the same close tolerances as in the Iosipescu- test. This test appears good but there are still uncertainties in the test results because of the influence of the notch parameters. An extensive analytical and experimental investigation of this test has been performed [7]. It has been shown that when an attempt is made to optimize the notch parameters to SH E AR TESTIN G O F COMPOSITES 611 obtain favourable stress distributions, the failure mode changes unexpectedly. The result is that the test section does n ot fail in a pure shear m ode. F ree edge effects have been pro- posed  as  the  cause  of  this  phen om en on .  F or  a  quasi- isotropic  graphite- epoxy  laminate, the 90°- sharp n otch appears  to give the best  result  in terms of  a  pure shear failure.  F urth er work  needs  to  be  don e  to  optimize  the  notch  parameters  for  orthotropic  materials. T ) F ig.  4.  Asymmetrical  four  point  bend  shear  specimen Photoelastic  Calibration  of  Birefringent  Orthotropic  M aterials In  recent  years,  th e  extension  of  transmission  photoelastic  techniques  to  transparent birefringent  orth otropic  composites  has  received  considerable  attention from  researchers. Such  materials  are  characterized  by  three  fundamental  photoelastic  constants. The  stress fringe  values  are f L , f T ,  a n d / i j ,  corresponding  t o  the  two  normal  stress  components parallel  and  perpen dicular  t o  the  major  material  symmetry  axis  and  to  the  shear  stress component.  While  these  three  photoelastic  properties  can  be  calculated  from  simple stress- strain  models  [8],  they  can  also  be  obtained  from  the  photoelastic  calibration  of tensile,  compressive  or  bending; coupon s.  If  the  fiber  orientation  (or  the  direction  of  the major  material  symmetry  axis)  is  parallel  or  perpendicular  to  the  specimen  axis,  then fi  a n d / r  are obtained, respectively.  As  th e application  of a  pure shearstress  is  not  straight- forward,  a third specimen with  an angle  of 45 degrees  between  the major  material  symmetry axis  and  the  specimen  axis  is  calibrated  in  tension.  The  resulting  stress- fringe  value f„, Ą is  used  to. calculate f L T   by  the  following  equation :  •   . The circular disk  specimen  th at is commonly used  to calibrate isotropic model  materials has not been  used  in  th e calibration  of  orthotropic model  materials  because  a  closed- form theoretical  solution  is  n ot  available.  The fringe  values f L   a n d / T  can  be  obtained  by  testing a  circular  disk  with  strain  gages  but f L T   cannot  be  determined. A  half- plane  specimen  with  photoelastic  coating  has  been  utilized  [9]  in  measuring the in- plane elastic  con stan ts  of  orthotropic composites.  The half- plane  specimen  has  also bean used for  simultaneous  measurement  of  orthotropic elastic  and  photoelastic constants [10], One half  of  the  specimen  is  utilized  for  th e measurement  of  elastic  constants  and the other  half  is  useful  for  photoelastic  observations.  A  sketch  of  the  specimen,  with  the 612 R.  PRABHAKARAN locations  of  the  strain  gages,  is  shown  in  Fig.  5.  Composite  laminates  are  heterogeneous materials  which  are  assumed  to  be  homogeneous  for  engineering  applications.  Usually average  properties  of  the  laminates  are  required.  A least  squares  procedure  that  uses over-determined experimental data is ideally suited for this type of measurement [111, stacked strain-gage rosette direction of • — E reinforcement - 2 0 0 mm • Fig. 5. Haff-plane specimen with strain gages ' •: ; The governing equation is written in terms of the required parameters in the general . ; • .•; • • :; • gk~ (A,B,C,D)~0. ! . ' • ( 2) where k = 1,2,..., M {M > 4) refers to particular points in the data field. The parameters to be evaluated are A, B, C and D. Expanding Eq. (2) in a Taylor's series, ' where i refers to the iteration-step number i and AA,AB, AC, AD are the corrections to the previous estimates of the corresponding parameters. Since* the desired result is (gk)i+t «* 0, Rewriting the above equation in matrix notation, where (4) .'•' ® . (6) SH E AR  TESTIN G   OF   COMPOSITES 613 8A 8B 8C 8D Solving  Eq.  (5), where 8B 8C 8t) A A AB AC AD tel (7) (8) (9) I n implementing  the above  procedure, initial  values  of A, B, C, D are  assumed  and the matrices [g] an d [b]  are  com puted. Then  the  error  vector [AE]  is  calculated  and  the esti- mates of A, B, C  an d D  are revised. Th e steps  are repeated until the convergence  is  satisfac- tory. Considering a load P applied  perpendicular  to  th e  edge  of  an  orthotropic  half- plane, with  the  major  material- symmetry  axis  parallel  t o  th e  loaded  edge  of the  half- plane,  the stress  com ponents  in  polar  coordinates  are given  [12]  by  ,•   •   •   • •   2P sin 9 0L2 — ! +  1 +  («! -  I)cos2(9a 2  + 1 +  ( «2 - 1)  C os20 < r f l , T r 0 = 0  • • • :;';  •   '•   ;  • •  '  (12) where i is  the thickness  of  the half- plane, 0 is the angle  from  the loaded  edge an d oc 1   and x 2 are  derived  elastic  con stan ts  given  by  '  • • • • ..• ,  ,,  ,..  a L ct 2   =   ErlF- 0Ci  +