The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization

Round 1

Reviewer 1 Report

The Maximum Stress Failure Criterion and the Maximum Strain Failure Criterion: Their Unification and Rationalization

Author; Shuguang L

 

Summary

This manuscript is well written with a clear structure. After introducing conventional stress and strain failure criterion, it proposes a unified maximum stress/strain criterion method. It is based on strain method, while trying to decouple the impact from other two direction, and then degrade to stress method under circumstance. The method is then carried out for further rationalization in transversely isotropic materials.

 

Observation

 

1, The idea of a unification is novel. And the Figure comparing conventional strain criterion and effective strain criterion is helpful. The red point, indicating experiment data, is a good counterexample. The question is, the revised method induces a big change of the critical number in one direction strain case (only x axis). In other words, is there any counterexample in the new parallelogram? More data points need to be shown here.

 

2, It would be better if the energy method like Tsai-Wu, Tsai-Hill are mentioned. Intuitively this method serves as a midway between simple stress/strain criterion and those criterions include parameter matching.

Author Response

Reviewer’s comment:

Summary

This manuscript is well written with a clear structure. After introducing conventional stress and strain failure criterion, it proposes a unified maximum stress/strain criterion method. It is based on strain method, while trying to decouple the impact from other two direction, and then degrade to stress method under circumstance. The method is then carried out for further rationalization in transversely isotropic materials.

 

Author’s response:

The author acknowledges the Reviewers positive endorsement.

 

Reviewer’s comment:

1, The idea of a unification is novel. And the Figure comparing conventional strain criterion and effective strain criterion is helpful. The red point, indicating experiment data, is a good counterexample. The question is, the revised method induces a big change of the critical number in one direction strain case (only x axis). In other words, is there any counterexample in the new parallelogram? More data points need to be shown here.

 

Author’s response:

It is true that the changes from the conventional failure envelope (rectangle) is more pronounced in one direction, i.e. the top and bottom sides of the rectangle have been tilted greatly. Less pronounced changes are also present in the other direction, i.e. the left and right side have also tilted although not as much as the top and bottom sides. These changes are dictated by the Poisson’ ratios of the material. As can be seen from the 1^st equation of (14), the effects of transverse strains on the longitudinal strain are through the minor Poisson’s ration, i.e. n_LE_T/E_L, which is usually significantly less than the major Poisson’s ration n_L, whilst the effects of longitudinal strain on the transverse strains are through the major Poisson’s ration n_L according to the 2^nd and 3^rd equations of (14). The new failure envelope (parallelogram) as shown in Figure 2 (previously Figure 1) is free from apparent anomalies. However, this should not be understood as being of perfect accuracy. The comment the Reviewer made has been addressed through the revision in Fig. 2 where a significant amount of information has been added and associated narrative lines 174~190 as highlighted.

 

The test data points involved are essential input data for all criteria, including the present one. On the issue of test data points, the purpose of Fig. 2 is not to show how well or badly the prediction matches the experiment. It is the fact that the theory (the maximum strain criterion) fails to reproduce the input data (the strength in fibre direction compression). Under uniaxial tension, the strain ratio is epsilon_1:epsilon_2=1:-nu_12, as indicated in the revised figure in order to clarify the position. The predicted failure would be at the green dot in a mode of transverse tension. Such an anomaly is a logical inconsistency in the theory, which is much more significant than lack of accuracy. It is the consistency issue the unification part of the paper is addressing rather than the accuracy as the author believes that before a theory can be presented in a consistent manner, accuracy is irrelevant.

 

Reviewer’s comment:

2, It would be better if the energy method like Tsai-Wu, Tsai-Hill are mentioned. Intuitively this method serves as a midway between simple stress/strain criterion and those criterions include parameter matching.

 

Author’s response:

The Tsai-Wu criterion has been incorporated in the case study as in the newly added Section 6 and compared with the present criterion in a new Figure 5.

Reviewer 2 Report

The author discusses the maximum strain/stress failure criteria and emphasizes on the combination of maximum strain failure criterion with maximum stress criterion. The author presents an approach of combining two criteria so that one can ignore using uniaxial failure strains directly. Although, the methods sounds interesting, I have the following comments that should be included in the paper:

• Failure criteria in composites may not be directly related to the uniaxial tensile data of the fibers or matrix materials. There are many simple and complicated failure criteria like Hill criterion, Tsai-Hill criteria, Tsai-Wu criterion, etc. for composite materials. Please compare the effectiveness of your approach with such composite failure criteria.
• Interfacial and interaply failure might occur in the unidirectional transversely isotropic composites (See below as an example). Please comment on the limitation of the presented method on different kinds of failure in such composite materials.

 

Mehrmashhadi, Javad, Ziguang Chen, Jiangming Zhao, and Florin Bobaru. "A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites." Composites Science and Technology 182 (2019): 107770.

Bobaru, F. L. O. R. I. N., J. A. V. A. D. Mehrmashhadi, Z. I. G. U. A. N. G. Chen, and S. I. N. A. Niazi. "Intraply fracture in fiber-reinforced composites: a peridynamic analysis." In ASC 33rd Annual Technical Conference & 18th US-Japan Conference on Composite Materials, Seattle, p. 9. 2018.

• Please explain the degree of interaction among stress and strain components discussed in lines 90-98 with equations.
• To better compare the failure envelopes shown in Figure 1, please test your method on a material listed in Table 1 and draw an in-scale graph.

 

 Note that the red dot in that Figure 1 does not have a description.

Author Response

Reviewer 2

Reviewer’s comment:

The author discusses the maximum strain/stress failure criteria and emphasizes on the combination of maximum strain failure criterion with maximum stress criterion. The author presents an approach of combining two criteria so that one can ignore using uniaxial failure strains directly. Although, the methods sounds interesting, I have the following comments that should be included in the paper:

Author’s response:

The Reviewers positive endorsement has been greatly appreciated.

 

Reviewer’s comment:

Failure criteria in composites may not be directly related to the uniaxial tensile data of the fibers or matrix materials. There are many simple and complicated failure criteria like Hill criterion, Tsai-Hill criteria, Tsai-Wu criterion, etc. for composite materials. Please compare the effectiveness of your approach with such composite failure criteria.

Author’s response:

The Reviewer rightly pointed out the availability of other failure criteria for composites. The most commonly employed criteria in engineering and in the literature have been reviewed in great depth in ref [3]. A much broader base and significant account of available criteria and theories can be found from the publications of WWFE-I~III, as referred to in references [6-8]. Clearer references have been made to these accounts in lines 45~50. The rationalised maximum stress criterion is compared with the rationalised Tsai-Wu criterion in the newly introduced Section 6.

 

Reviewer’s comment:

Interfacial and interaply failure might occur in the unidirectional transversely isotropic composites (See below as an example). Please comment on the limitation of the presented method on different kinds of failure in such composite materials. Mehrmashhadi, Javad, Ziguang Chen, Jiangming Zhao, and Florin Bobaru. "A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites." Composites Science and Technology 182 (2019): 107770.

Author’s response:

The maximum stress/strain criteria are meant to be criteria for material failure, like most available failure criteria in the literature. For structural applications, such as a laminated construction, it will have to be dealt with in a ply by ply manner, i.e. a ply is treated as a material. An appropriate statement has been added in the Introduction as highlighted in lines 51~60.

 

Reviewer’s comment:

Bobaru, F. L. O. R. I. N., J. A. V. A. D. Mehrmashhadi, Z. I. G. U. A. N. G. Chen, and S. I. N. A. Niazi. "Intraply fracture in fiber-reinforced composites: a peridynamic analysis." In ASC 33rd Annual Technical Conference & 18th US-Japan Conference on Composite Materials, Seattle, p. 9. 2018.

Please explain the degree of interaction among stress and strain components discussed in lines 90-98 with equations.

To better compare the failure envelopes shown in Figure 1, please test your method on a material listed in Table 1 and draw an in-scale graph.

Author’s response:

Thanks for the suggestion. To elaborate the point made, Figure 1 has been added illustrate such interactions, assisted with relevant equations as shown in Figure 1, with relevant text revised appropriately as highlighted in lines 114-123.

Figure 3 has been added to this effect involving two of the materials listed in Table 1 with necessary narrative in lines 281~284 as highlighted.

Reviewer’s comment:

Note that the red dot in that Figure 1 does not have a description.

Author’s response:

A key has been added for the red dot along with other improvements.

Round 2

Reviewer 2 Report

Thank you for revising the paper. My comments have been addressed. I only have two minor comments:

1- Excel graphs are unacceptable in scientific journal papers. Please use software like Matlab for all figures. You can change Tau_23 to a symbol/equation form after that.

2- Thank you for adding a section (lines 54-60) and discuss other types of failure. Please refer those two references in my previous comments (see below).

Mehrmashhadi, J., Ziguang C., Jiangming Z., and Bobaru, F. "A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites." Composites Science and Technology 182 (2019): 107770.

Bobaru, F., Mehrmashhadi, J., Ziguang, C., and Niazi, S. "Intraply fracture in fiber-reinforced composites: a peridynamic analysis." In ASC 33rd Annual Technical Conference & 18th US-Japan Conference on Composite Materials, Seattle, p. 9. 2018.

Author Response

The Reviewer's comments have been addressed as far as appropriate as detailed below.

(1)  Figs 3 and 5 have been improved. 

(2)  The first reference the Reviewer kindly provided has been referred to in the revised version as submitted whilst mentioning intra-ply failure.  The second reference has been referred to in the first reference and the relevant contents to the present paper have also been reproduced in the first reference.  I therefore believe that it is sufficient by citing the first.

(3)  A few typos in the manuscript have been corrected.