Mechanical properties of natural rubber vulcanizates in finite deformation

<jats:title>Abstract</jats:title><jats:p>Mechanical properties of four kinds of natural rubber vulcanizates differing in vulcanization conditions, and consequently in degree of crosslinking (having values of the Mooney‐Rivlin constant <jats:italic>C</jats:italic><jats:sub>1</jats:sub> ranging from 0.68 to 1.98) were observed under orthogonal biaxial stretching in a range of strain invariants <jats:italic>I</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub> from 3.4 to 9.0 (extension ratios λ<jats:sub><jats:italic>i</jats:italic></jats:sub> from 0.7 to 3.0). The results obtained were analyzed by two methods. One method employed the Valanis‐Landel postulate that the strain‐energy function <jats:italic>W</jats:italic>(λ<jats:sub>1</jats:sub>, λ<jats:sub>2</jats:sub>, λ<jats:sub>3</jats:sub>) is a separable symmetric function of the principal extension ratios, i.e., <jats:italic>W</jats:italic>(λ<jats:sub>1</jats:sub>,λ<jats:sub>2</jats:sub>,λ<jats:sub>3</jats:sub>) = <jats:italic>w</jats:italic>(λ<jats:sub>1</jats:sub>) + <jats:italic>w</jats:italic>(λ<jats:sub>2</jats:sub>) + <jats:italic>w</jats:italic>(λ<jats:sub>3</jats:sub>); the other utilized the contour plots of ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>, <jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>1</jats:sub> and ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>, <jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>2</jats:sub> surface within the (<jats:italic>I</jats:italic><jats:sub>1</jats:sub>, <jats:italic>I</jats:italic><jats:sub>2</jats:sub>) domain. The postulate for <jats:italic>W</jats:italic> was examined in detail with good agreement with experimental results. The dependences of ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>, <jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>1</jats:sub> and ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>, <jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>2</jats:sub> surfaces on the degree of crosslinking and temperature were further investigated, with the following conclusions. The surfaces have fairly steep slopes for the region of relatively small deformation (i.e., <jats:italic>I</jats:italic><jats:sub>1</jats:sub> < 5) and become flat with increasing <jats:italic>I</jats:italic><jats:sub>i</jats:sub> for all the test specimens. The slope becomes less steep with decreasing degree of crosslinking. The values of ∂<jats:italic>W</jats:italic>/∂<jats:italic>I</jats:italic><jats:sub>1</jats:sub> increase linearly and the ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>,<jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>2</jats:sub> surface becomes flat, both with increasing temperature: i.e., the temperature dependence of ∂<jats:italic>W</jats:italic>/∂<jats:italic>I</jats:italic><jats:sub>1</jats:sub> further depends on <jats:italic>I</jats:italic><jats:sub><jats:italic>i</jats:italic></jats:sub>. The ∂<jats:italic>W</jats:italic>(<jats:italic>I</jats:italic><jats:sub>1</jats:sub>,<jats:italic>I</jats:italic><jats:sub>2</jats:sub>)/∂<jats:italic>I</jats:italic><jats:sub>2</jats:sub> surface has a maximum near 40°C.</jats:p>