Abstract
Tensorial-type failure criteria with linear and quadratic terms are used to calculate the strength of paperboard under plane stress. Theoretical predictions and experimental data are correlated in all four quadrants of biaxial normal stress with various levels of shear. Several methods are examined for determining the interaction coefficientF 12. Comparisons are made with optimum values obtained from least-squares analyses. The best analytical-experimental agreement at all levels of shear is obtained approximately by using coefficientF 12 equal to zero. The sensitivity ofF 12 to errors in experimental input data is also studied. Reliable correlation with experiment, as well as operational simplicity, make these criteria attractive for predicting the strength of paperboard.
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Abbreviations
- E :
-
elastic modulus
- F ij :
-
strength coefficients
- P :
-
on-axis biaxial tensile strength
- P′ :
-
on-axis biaxial compressive strength
- S :
-
on-axis shear strength
- S 45 :
-
positive shear strength of a 45-deg off-axis coupon
- S′ 45 :
-
negative shear strength of a 45-deg off-axis coupon
- U :
-
uniaxial tensile strength of a 45-deg off-axis coupon
- U′ :
-
uniaxial compressive strength of a 45-deg off-axis coupon
- X :
-
uniaxial tensile strength in the MD
- X′ :
-
uniaxial compressive strength in the MD
- Y :
-
uniaxial tensile strength in the CD
- Y′ :
-
uniaxial compressive strength in the CD
- ν:
-
Poisson's ratio
- σ:
-
normal stress
- τ:
-
shear stress
- x, y, z :
-
coordinate directions
- U θ :
-
uniaxial tensile strength of an off-axis coupon at angle θ
- U′ θ :
-
uniaxial compressive strength of an off-axis coupon at angle θ
- σ c1 , σ c2 :
-
coordinates of the center of the analytical failure envelopes
- S c :
-
maximum unfailed level of shear stress
- MD:
-
machine direction
- CD:
-
cross-machine direction
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Suhling, J.C., Rowlands, R.E., Johnson, M.W. et al. Tensorial strength analysis of paperboard. Experimental Mechanics 25, 75–84 (1985). https://doi.org/10.1007/BF02329129
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DOI: https://doi.org/10.1007/BF02329129