Overcoming the Dependence of the Yield Condition on the Absence of Macroscopic Structures

Round 1

Reviewer 1 Report

The work raises a significant problem of limitations of standard measures for determining yield strength for materials with strong macroscopic structures. The authors proposed a new method that is a solution to this problem.

To verify their proposition, plain and dimpled steels were tested in tension. Moreover, the authors incorporated from literature data for porous Ti alloy and lattice steel materials under tensile load. Athors compared the standard methods for quantification of yield strength with the non-standard for all proposed materials. Therefore it was possible to indicate the limitation of the standard measures. It was shown that the second derivative of stress with respect to strain allows quantifying the yield strength non-arbitrary. It was also shown that the proposed methodology is in good agreement with the standard approach in the case of discontinuous yield.

Small remarks:

Fig 10, 12, and 14. I would recommend putting the colors in the picture analogically. It means, for example, that the derivative yield is orange in Fig. 10 and red in Fig. 12. It makes some confusion.

Fig 10 The y-axis is stress, but the correct units are MPa, not MPA.

In all Figures, please decide whether axis captions are uppercase or lowercase.

Fig. 11 and 12, there are missing units on the axes

Fig 2, 4, 10, 13: Why does the measured stress-strain curve not start from 0 MPa?

Fig 14 The elastic moduli is not fitted from 0 (the 0.2% offset also is not from 0 MPa), but on the e.g., Fig 10, you start from 0 MPA for elastic modulus and 0.2% offset. Could you please comment?

Author Response

Dear Reviewer 1

Fig 10, 12, and 14. I would recommend putting the colors in the picture analogically. It means, for example, that the derivative yield is orange in Fig. 10 and red in Fig. 12. It makes some confusion. - DONE

Fig 10 The y-axis is stress, but the correct units are MPa, not MPA. - DONE

In all Figures, please decide whether axis captions are uppercase or lowercase. - DONE

Fig. 11 and 12, there are missing units on the axes

Fig 2, 4, 10, 13: Why does the measured stress-strain curve not start from 0 MPa?

ANSWER: 

Where the available data does not extend to 0MPa, that which is available has been provided without modification.

Fig 14 The elastic moduli is not fitted from 0 (the 0.2% offset also is not from 0 MPa), but on the e.g., Fig 10, you start from 0 MPA for elastic modulus and 0.2% offset. Could you please comment?

ANSWER: 

Due to the geometry of both the dimpled samples and the clamps on the testing rig, a small amount of additional displacement is seen in early loading for some samples as the clamps bite into the sample. In some cases, this necessitates ignoring the low-stress data when determining the Elastic Modulus to produce an accurate representation of the material behaviour. The 0.2% offset is a direct offset from the initial fit and so does not start at 0MPa because the line representing the Elastic Modulus does not. 

Fig. 10 is external data and the trend shows a clear intersect with 0,0. Therefore, the trend line was extended to 0,0 for illustrative purposes.

Kind Regards

the authors

Reviewer 2 Report

This is an article where the authors propose an interesting approach for determining the unified yield strength. The idea is to calculate the second derivative of the stress curve with respect to strain. The authors conducted a series of experiments and demonstrated the efficiency of the proposed idea. The article is well written and its results are of both scientific and practical interest. The reviewer recommends the article for publication after addressing the following minor concerns.

1. Very often, experimental stress-strain curves contain noise, which can lead to certain difficulties in calculating derivatives. Do the authors offer methods for local smoothing of experimental data for calculating derivatives?

2. On fig. 6 shows a flat tensile test specimen. Do the authors note any peculiarities of applying their approach to determining the yield strength for cylindrical and flat specimens?

3. It is desirable to improve the quality of the Figs. Since authors are talking about the yield strength, it makes sense to show values along the deformation axis up to 1%. It is also necessary to check the labels to the axes, "Stress, MPa", "Strain, %".

4. Did the authors check the compliance of the elastic moduli of the materials used in the tests with their standard values? Sometimes it seems that the modulus of elasticity is significantly lower than it should be.

Author Response

Dear Reviewer 2

1. Very often, experimental stress-strain curves contain noise, which can lead to certain difficulties in calculating derivatives. Do the authors offer methods for local smoothing of experimental data for calculating derivatives?

2. We have made no comment on this though I have noticed noise present in our data. Figs. 8 (plain steel) and 9 (external data) are good examples of what this looks like. Often this noise has produced additional, pronounced turning points but in all cases that we have assessed, the most pronounced turning point clearly coincides with what is the apparent yield point when qualitatively assessing the stress-strain curve as a whole.

    

   It may be worth noting that the derivative yield has been successfully applied using either the finite difference method or by differentiation of a best fit curve. Provided that the best fit curve covers a region that contains the macroscopic yield point and provided that the fit is of a high quality, this method also works as reported. That said, the finite difference method does not require the aforementioned judgements and is therefore a more robust approach.

   
   
   2. On fig. 6 shows a flat tensile test specimen. Do the authors note any peculiarities of applying their approach to determining the yield strength for cylindrical and flat specimens?

   Samples of other shapes have not been considered in the present work.

   
   
   3. It is desirable to improve the quality of the Figs. Since authors are talking about the yield strength, it makes sense to show values along the deformation axis up to 1%.

   The figure axes have been scaled to try to give a clear illustration of small-scale variation while still illustrating large-scale behaviours indicative of the type of yield (discontinuous, continuous, severely continuous). In the case of Fig. 8, this leads to a relevant scale of 0 - 1% strain. In other cases, e.g. Fig. 11, a smaller range ( 0 - 0.08% ) is necessary to clearly illustrate the present behaviour.

3. It is also necessary to check the labels to the axes, "Stress, MPa", "Strain, %". - DONE
   
   4. Did the authors check the compliance of the elastic moduli of the materials used in the tests with their standard values? Sometimes it seems that the modulus of elasticity is significantly lower than it should be.

Compliance of this sort has not been checked since the material grade used (DX51D+Z/ZF) is a particularly variable grade of mild steel. The specifications provide only for a minimum yield strength and, anecdotally, this is usually exceeded by a large margin.

Kind Regards

the authors