Citation: Koutiri, I.; Andreau, O.;
Peyre, P. Multi-Scale Approach of
HCF Taking into Account Plasticity
and Damage: Application to LPBF
Materials. Appl. Mech. 2022, 3,
544–559. https://doi.org/10.3390/
applmech3020032
Received: 17 March 2022
Accepted: 25 April 2022
Published: 29 April 2022
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Article
Multi-Scale Approach of HCF Taking into Account Plasticity
and Damage: Application to LPBF Materials
Imade Koutiri *, Olivier Andreau and Patrice Peyre
Laboratoire Procédés et Ingénierie en Mécanique et Matériaux PIMM, Arts et Métiers Institute of Technology,
CNRS, Cnam, HESAM Université, 75013 Paris, France; andreau.olivier@gmail.com (O.A.);
patrice.peyre@ensam.eu (P.P.)
* Correspondence: imade.koutiri@ensam.eu
Abstract:
Laser additive manufacturing enables economical production of complex lightweight
structures. To realize the potential benefits of additive manufacturing technology in industrial
applications, the fatigue performance of parts additively manufactured materials must be modelized.
The aim of this paper is to present a new modeling approach combining plasticity and damage,
and appropriate for as-built Laser-Powder Bed Fusion (LPBF) structures. The model presented is
an extension of the Dang Van criterion, including damage, defined as porosity in the case of LPBF.
Attention is focused on the integration of damage in a fatigue criterion using the concept of elastic
shakedown. Finally, the case of 316L will illustrate the results of the model by fatigue tests with
deterministic defects.
Keywords: material fatigue; LPBF; 316L; defects; damage
1. Introduction
Additive manufacturing has now reached a sufficiently good maturity and robustness
to fit with industrial criteria, with the use or not of post-building treatments (heat treatments,
hot isostatic pressing). In the laser powder bed fusion (LPBF) process, a powder layer is
spread on a building platform and a laser beam melts selectively around the deposited layer,
each individual laser path being composed of a contour and a hatching phase. The platform
is then lowered down by a 20
µ
m to 100
µ
m height and a new powder layer is applied.
This single layer LPBF procedure is then repeated for a number of layers to reach the final
3D shape. At the end of the whole fusion stage, the built part is removed from the powder
bed and de-powdered.
The most common defects observed systematically on LPBF are porosities (lacks-
of-fusion LOF or blowholes) which can impact the material properties and specifically
lower fatigue resistance. Such porosities are dependent on many process parameters (laser
power, scan speed, hatch distance, etc.) which can be combined into volume energy density
(J/mm
3
) parameters traducing the amount of laser energy injected into the built material.
Additionally, the scan strategy (chess, stripes, etc.) also plays a major role versus the final
porosity rate and residual stress distribution.
Classical fatigue mechanisms occurring on L-PBF parts are rather well documented in
the literature [
1
]. For instance, it is well known that fatigue crack initiation in the case of
LPBF is controlled by porosities, spatters and other microstructural heterogeneities. One of
the specific trends of the LPBF process is the possibility of real-time detection and analysis
of these defects during the process which is difficult for the casting process. The modeling
of defects must be considered to adequately design components and to be able to estimate
the final fatigue properties.
In High Cycle Fatigue (HCF), many multiaxial fatigue criteria can be found in the
literature. Some of them are based on phenomenological approach such as the Sines [
2
]
or Crossland [
3
] criterions. In terms of HCF of polycrystalline metallic materials, it is
Appl. Mech. 2022, 3, 544–559. https://doi.org/10.3390/applmech3020032 https://www.mdpi.com/journal/applmech
