SAMPE Journal - September/October 2019 - 38

FEATURE / THERMOPLASTIC COMPOSITES FROM ADDITIVE MANUFACTURING
The standard "Max-Stress" failure criteria
is shown in Figure 13. Here, FS stands for "factor-of-safety" with the t and c superscripts denoting tension and compression failure, respectively.
A factor of safety ≤1 indicates failure, otherwise, the
analytical failure criteria predicts no failure.
The Max-Stress FD criteria differs from the traditional maximum stress criteria, in that, if a laminate has a variety of fiber directions (e.g. not unidirectional) we switch to the fiber dominated failure
mode to predict failure, and, we ignore predictions
of matrix failure when fibers transverse the matrix
in nearby layers (or regions). Figure 14 shows comparison of standard "Max-Stress FD", "Tsai-Hill 3D"
and the "Max-Stress" with AREVO data for three
lay-up configurations. The Max-Stress FD provides the best correlation, with the standard "MaxStress" and "Tsai-Hill 3D" criteria being overly conservative for QI and [0/60°/-60°]s.
In Figure 15 the strength data of CF/PEEK material with fiber volume content of 60% measured
by Jen & LEE [27] is compared with the predictions
based on the Max-Stress FD and Tsai-Hill 3D criteria. It is seen that the measured results have
higher strength levels compared with the 50 vol%
DED materials introduced in the previous sections,
which is mainly due to the higher fiber content and
improved consolidation from the autoclave process. The data also shows that the Max-Stress FD
failure criteria provides reasonable assessment of
laminate strength similar to that obtained using
Tsai-Hill 3D. Jen & Lee used the Tsai-Hill failure criteria for their study of static and fatigue strength.
Box Beam Stress Analysis and Strength
Assessment
Box beams are common structural elements. Being able to customize and make small production
lots or even one-offs represents a manufacturing
opportunity for Additive Manufacturing. The box
beam geometry shown in Figure 16 has a length
of 300 mm with nominal wall thickness of 2 mm.
Depending upon the use case and loading, different printing strategies should be utilized. The
proposed design was analyzed using company
design software Pathfinder with material properties presented in the above sections along with the
previously discussed Max-Stress FD failure criteria.
Displacements, stresses and failure were predicted.
This analysis showed that depending upon the precise support conditions at the end, we may not realize the full strength of the design. It was predicted
(based on the expected boundary conditions) that
large shear stresses near the support precluded
development of the full box beam strength. These

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Figure 13. Standard max-stress failure criteria.

Figure 14. Comparison of AREVO measured strength and predicted results
with Max Stress FD, Max-Stress, and Tsai-Hill failure criteria, showing the
strength results obtained from Max Stress FD criteria agree best with the
measured data.

shear stress concentrations which are induced due
to the support conditions are shown in the lower
portion of Figure 16. Based upon these predictions,
the failure was predicted to occur near the support
at a level of 10 kN.
Figure 17 shows the box beam previously analyzed as built (a) and under 3-point bending load
(b). The average observed failure load for three
samples tested was 11.4 kN. The observed failure
load matches well with the predicted failure load
and represents an 11% error in prediction, with the
prediction being a conservative (underestimated)

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SAMPE Journal - September/October 2019

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