# Calibration of Failure Criteria for Additively Manufactured Metallic Materials

## Abstract

**:**

## 1. Introduction

## 2. Influence of the Stress State on Ductility

_{m}stands for mean stress (hydrostatic part of stress tensor—average value of the three principal stresses) and σ

_{eq}stands for equivalent stress (some function of the second invariant of the stress tensor). In the case of Huber–Mises hypothesis, equivalent stress is given by the following formula:

_{2}is the second invariant of stress deviator.

_{eq}stands for equivalent strain. The integration of the equivalent strain increments along the deformation path in the strain space gives the result as a so-called Odquist parameter [10]:

_{1}, must be determined). This significantly simplifies the calibration procedure.

_{2}, calibration of this criterion requires at least two tests to be performed in different stress states.

## 3. Procedure and Equipment

_{1}) must be determined to calibrate criterion (5). This criterion is easy to calibrate and accounts for the influence of the stress state on the failure strain. Bearing in mind all the mentioned difficulties described in [4], using the simple definition (5) and a more accurate and credible calibration procedure may be advantageous. An appropriate loading scheme must be selected to maintain the constant value of the stress triaxiality factor during the entire test. To avoid strain localization, it is very convenient to apply pure shear.

## 4. Calibration of Selected Criteria for 316L Alloy Steel

_{1}is, in this case, equal to plastic strain intensity at failure. To obtain its value, maximum permanent (plastic) equivalent strain at the surface of the gauge part had to be found based on the angle of twist of the gauge part measured on microscope. For the geometry of the used specimen, shear angle was found to be φ = 0.14 rad. Based on this value and assuming proportional strain path in the strain space, the equivalent failure strain was found to be:

_{1}in Equation (6), the value of the second constant (C

_{2}) can be determined. For this conservative approach, a calibrated criterion takes the following form:

## 5. Summary and Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**Two versions of setup for the determination of failure strain. Version (

**a**) with an inductive heating coil (3) is suitable for elevated temperatures. Version (

**b**) can be used for elevated, as well as lowered, temperatures.

**Figure 2.**Specimen after the torsional test. Marked line, parallel to the specimen axis before test is inclined to specimen axis. Angle between axis and marked line is shear angle.

**Figure 3.**Tensile characteristics of 316L AM alloy steel with picture of broken specimen. Non-linearity of the characteristics is clearly visible.

**Figure 4.**Calibrated criteria with graphical representation: Hancock–Mackenzie—broken line; modified criterion—solid line.

Cr | Ni | Mo | C | Mn | Cu | P | S | Si | N | Fe |
---|---|---|---|---|---|---|---|---|---|---|

17–19 | 13–15 | 2.25–3 | 0.03 | 2.0 | 0.5 | 0.025 | 0.01 | 0.75 | 0.1 | balance |

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**MDPI and ACS Style**

Socha, G.
Calibration of Failure Criteria for Additively Manufactured Metallic Materials. *Materials* **2021**, *14*, 3442.
https://doi.org/10.3390/ma14133442

**AMA Style**

Socha G.
Calibration of Failure Criteria for Additively Manufactured Metallic Materials. *Materials*. 2021; 14(13):3442.
https://doi.org/10.3390/ma14133442

**Chicago/Turabian Style**

Socha, Grzegorz.
2021. "Calibration of Failure Criteria for Additively Manufactured Metallic Materials" *Materials* 14, no. 13: 3442.
https://doi.org/10.3390/ma14133442