Biaxial strength of paperboard predicted by hill-type theories

Abstract

Paperboard strength under biaxial normal plus shear stresses is predicted using Hill-type criteria (including TsaiHill, Norris, Fischer, and Ashkenazi). Results are compared throughout ail four quadrants with experimental data obtained from on-and off-axis uniaxial coupons, cylinders, and cruciform specimens. The Norris and Fischer theories predict observation quite well except at higher values of shear stress where they become too conservative. The Tsai-Hill theory is conservative throughout. Simplicity of both analysis and implementation, plus need for only minimal experimental input data, are significant advantages of Hill-type criteria. Moreover, their reliability for paper is comparable to that of other published results. Other strength theories will be addressed in subsequent papers.

A new approach of three-dimensional strength theory for anisotropic materials

“…These theories do not correlate well with the data. On the other hand, the strength characteristics of these materials can be correlated very well with the present theory, using (1), with coefficients A, given in (8).…”

“…The biaxial strength of a paperboard has been studied experimentally and compared to the predictions by using several failure criteria by Rowlands and Suhling et al [8,9]. From the results of these studies, we see that Hill-type failure criteria give unsatisfactory prediction at high level of shear stress.…”

“…where coefficients A~ have been given in any one of (2), (4), (6) or (8). The strengths in the z-axis can be expressed in a form similar to (1):…”

“…If we consider only the first term of (19), i.e., C O ¢ 0 and C, = 0 for n >~ 1 and evaluate Fxy individually for each stress quadrant, the correlation between the prediction and the data is excellent. The variation of the Fxy (Table 1) for the four quadrants is much smaller than that of the Hill-type failure criteria [8]. Using the Fxy values listed in Table 1, the strength of the paperboard under general combined loading can be predicted using their principal stresses.…”

Comparison of Failure Criteria for Wood in Tensile-Shear Stress State

“…It follows that strength theories developed for artificial composites can be used for prediction of wood strength [1,2]. Unfortunately, for some of these theories, it may be difficult to obtain specific coefficients experimentally, let us mention the issue of the interaction term [3][4][5]. All strength parameters may not be viewed in a deterministic way.…”