Unconstrained Ends P M Constrained Ends FIGURE 9.3 FIGURE 9.2 Influence of gripped end regions on deformation Off-axis coupon under uniform axial stress. of off-axis specimen [2]. 9.2 Influence of End Constraint As first pointed out by Halpin and Pagano [2],most test machines used in testing laboratories employ rigid grips that constrain the shear deformation illustrated in Figure 9.2.As a result,the specimen assumes a shape schematically illustrated in Figure 9.3 [2].To quantify the influence of gripping on the response of an off-axis tension specimen,Halpin and Pagano [2]performed a stress analysis of a constrained coupon and obtained the following expressions for the shear strain and longitudinal strain at the specimen centerline. Yxy=S1eC2-S66Cow2/4 (9.10a) ex=5C2-51Cow2/4 (9.10b) with 125160 C=3w25,56-5+25,民 (9.11a) C。-(356w2+52) C2=1256 (9.11b) where eo =AL/LG (elongation/gage length)and w and LG are specimen width and gage length,respectively(Figure 9.1). ©2003 by CRC Press LLC9.2 Influence of End Constraint As first pointed out by Halpin and Pagano [2], most test machines used in testing laboratories employ rigid grips that constrain the shear deformation illustrated in Figure 9.2.As a result, the specimen assumes a shape schematically illustrated in Figure 9.3 [2]. To quantify the influence of gripping on the response of an off-axis tension specimen, Halpin and Pagano [2] performed a stress analysis of a constrained coupon and obtained the following expressions for the shear strain and longitudinal strain at the specimen centerline. (9.10a) (9.10b) with (9.11a) (9.11b) where ε0 = ∆L/LG (elongation/gage length) and w and LG are specimen width and gage length, respectively (Figure 9.1). FIGURE 9.2 Off-axis coupon under uniform axial stress. FIGURE 9.3 Influence of gripped end regions on deformation of off-axis specimen [2]. 2 y x σ x x σ w LG P P M V Constrained Ends Unconstrained Ends 1 γ xy = − S C S Cw 16 2 66 0 2 4 εx = − S C S Cw 11 2 16 0 2 4 C S w SS S SLG 0 16 0 2 11 66 16 2 11 2 12 3 2 = ( ) − + ε C C S 2 Sw SLG 0 16 66 2 11 2 12 = + ( ) 3 TX001_ch09_Frame Page 134 Saturday, September 21, 2002 5:01 AM © 2003 by CRC Press LLC