6-14 DESIGN OF LAMINATES 



Fig. 6-7 shows the relation that exists between the various physical constants and the 

 angle to the warp for a laminate in tension made of mat reinforcement. It is readily esta- 

 blished that mat reinforcement produces an isotropic laminate, i. e. , one that has equal 

 properties at all angles. 



Fig. 6-8 is similar to Fig. 6-7 except that it represents a mat laminate in compression. 



Figs. 6-9 to 6-12 show the factors that are to be used in determining the elastic con- 

 stants Et, G12, and °12 f° r 10 ounce cloth and 25-27 ounce woven roving laminates. The 

 influence of the angle of loading or the angle between direction of stress and the longitudinal 

 axis, is clearly indicated. 



In an orthotropic laminate, shear and direct stress cause shear and direct strains. These 

 strains, at various angles, can be found by substituting the constants from the curves for 

 m^ and n^ in equations 6. 4, 6. 6 and 6. 7. 



In all of these graphs the angle degree is the longitudinal direction or the warp direc- 

 tion of the cloth and woven roving reinforcements. 



The following examples demonstrate the procedure to be followed in using these graphs. 



DESIGN EXAMPLE 6-1. TENSILE PHYSICAL PROPERTIES OF MAT 

 AND 10 OUNCE CLOTH LAMINATES AT 30 DEGREES TO WARP 



Determine the tensile physical properties at 30 degrees to the warp for the materials 

 shown in Figs. 6-7 and 6-9. 



The graphs show the relationships that exist for such constants as modulus of elasticity 

 E, modulus of rigidity G, Poisson's ratio o, and shear strain constants m-^ and n^. Constants 

 m.1 and m? apply to orthotropic materials only. 



a. Modulus of Elasticity 



The value of E, =E-i <>can be found as follows: 



For mat laminate; from Fig. 6-7, E = 1.00 or E x = 1.00 E = E. 



This indicates that E]_ at a specific angle is equal to E at degrees at all times. This 

 is always the case for an isotropic material. 



For 10 ounce cloth laminate, from Fig. 6-9 

 = 0.63h (Value at 30°) 



El 



E x = E 30 o „ 0>63U E L 



E 3Q o = 0.63li x 1.95 x 106 = 1.236 x 106 psi 

 Modulus of Rigidity G: 



n 



'or mat laminates, from Fig. 6-7 the plot indicates that — = O.lihk = a constant, 

 This apain is true for isotropic materials. E 



