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Cyclic R‐Curve Measurements for Structural Metallic Alloys

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Advanced Engineering Materials
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Luca Patriarca
Luca Patriarca
Luca Patriarca
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Antonio D'Andrea at École de Technologie Supérieure
Antonio D'Andrea
Matteo Cova
Matteo Cova
Matteo Cova
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Lorenzo Rusnati at Politecnico di Milano
Lorenzo Rusnati
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Abstract and Figures

Fractures nucleated from defects and subjected to cyclic loading can experience propagation for a range of stress intensity factor ΔK well below the so‐called long crack threshold. This phenomenon is attributed to the development of crack closure mechanisms which may differ from those observed in laboratory tests conducted in accordance with current standards. Cracks originating from material defects require a specific degree of extension to develop the plastic wake, thus achieving a stabilized condition called the long crack threshold. However, in certain materials, this stabilization length can extend up to several millimeters, effectively encompassing a significant portion of the component's fatigue life. Therefore, understanding and quantifying the development of ΔKth with crack extension is important for implementing a reliable assessment procedure based on the fracture mechanics theory. Herein, R‐curve measurements are presented for five distinct structural metallic alloys widely used in various industrial applications. Additionally, the impact of load ratio is investigated, providing a comprehensive analysis of fatigue crack resistance in terms of the R‐curve concept. This study underscores the necessity of ruling new experimental techniques to measure and implement the long crack threshold, thereby ensuring the development of a reliable and robust framework for fatigue assessment.
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Cyclic
R
-Curve Measurements for Structural Metallic Alloys
Luca Patriarca,* Antonio D’Andrea, Matteo Cova, Lorenzo Rusnati,
and Stefano Beretta
1. Introduction
The concept of fatigue crack threshold has garnered significant
interest over the last years due to the strong effect induced by
several factors, including microstructure, load ratio, sources of
crack closure, load history, etc. The complexity arising from these
diverse factors makes the formulation of a comprehensive crack
threshold model challenging. One practical approach to include
most of these factors into a tool suitable for industrial
applications is the use of the cyclic
R-curve.
[1,2]
The cyclic R-curve describes the
increase of the crack threshold ΔK
th
with
the crack extension Δa, and it was initially
observed in the 1980s.
[3–6]
The R-curve
allows to model the behavior of physically
short-cracks that are mainly governed by
the build-up of the closure mechanisms.
The crack closure sources are generally
induced by irreversible local mechanisms,
such as residual plastic strains, contact
between rough crack surfaces, and external
or internally-produced (i.e., by oxidation
processes) debris.
[7]
These factors are
closely linked to the specific alloys under
investigation. In particular, the early stages
of crack propagation are influenced by the
plasticity-induced crack closure, highlight-
ing the key role of the mechanical behavior
of the alloy. In this context, this study
presents R-curve measurements for five
significant metallic alloys widely employed
in various industrial applications.
The long crack threshold ΔKstab
th mea-
surement is ruled by the ASTM E647
standard.
[8]
In the present study, the apex stab is adopted to refer
to the stabilized crack propagation curve. This condition, accord-
ing to the ASTM E647 standard, is reached when the crack is first
propagated under a constant amplitude (CA) step up to crack
growth rates of 10
8
m cycle
1
and then decreased following a
load reduction (LR) procedure to reach the crack arrest point.
As evidenced by several literature works, the final threshold
ΔKstab
th is severely affected by the initial ΔKand by the crack
extension that occurred from the precrack condition.
[9–11]
This
evidence was clearly shown by Pippan et al. in ref. [12] where
the stepwise increase of load amplitude after compression pre-
cracking procedure was seen to provide lower threshold values.
It is important to note that the plasticity developed during
classical precracking strategies (i.e., with positive load ratio)
and the subsequent plastic wake produced during the initial
CA step both exerted a significant effect on crack propagation
and, consequently, on the measured threshold. To overcome this
problem, researchers have adopted specimen precracking under
fully compressive loadings (CP), taking advantage of the tensile
residual stresses generated inside the notch-tip plastic region
formed within a fully compressive load.
[10,11]
This precracking
strategy enables to start a crack propagation test with a nominally
closure-free crack, thus approaching the ideal condition of a
crack nucleated from a defect in a component. However, despite
the advantage given by CP in limiting the load history effect, the
L. Patriarca, L. Rusnati, S. Beretta
Department of Mechanical Engineering
Politecnico di Milano
via La Masa 1, 20156 Milano, Italy
E-mail: luca.patriarca@polimi.it
A. D’Andrea
Department of Mechanical Engineering
École de technologie supérieure
1100 Notre-Dame Street W, Montreal, Quebec H3C 1K3, Canada
M. Cova
R&D, Tiles Business Unit
SACMI IMOLA S.C.
Via Selice Provinciale 17/A, 40026 Imola, Italy
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adem.202400447.
DOI: 10.1002/adem.202400447
Fractures nucleated from defects and subjected to cyclic loading can experience
propagation for a range of stress intensity factor Δ
K
well below the so-called long
crack threshold. This phenomenon is attributed to the development of crack
closure mechanisms which may differ from those observed in laboratory tests
conducted in accordance with current standards. Cracks originating from
material defects require a specific degree of extension to develop the plastic wake,
thus achieving a stabilized condition called the long crack threshold. However, in
certain materials, this stabilization length can extend up to several millimeters,
effectively encompassing a significant portion of the component’s fatigue life.
Therefore, understanding and quantifying the development of Δ
K
th
with crack
extension is important for implementing a reliable assessment procedure based
on the fracture mechanics theory. Herein,
R
-curve measurements are presented
for five distinct structural metallic alloys widely used in various industrial
applications. Additionally, the impact of load ratio is investigated, providing a
comprehensive analysis of fatigue crack resistance in terms of the
R
-curve
concept. This study underscores the necessity of ruling new experimental
techniques to measure and implement the long crack threshold, thereby ensuring
the development of a reliable and robust framework for fatigue assessment.
RESEARCH ARTICLE
www.aem-journal.com
Adv. Eng. Mater. 2024,26, 2400447 2400447 (1 of 15) © 2024 Wiley-VCH GmbH
... The study of crack closure has been active for several decades from theoretical, experimental, and simulation perspectives [7][8][9][10][11]. Gradually, we could see these efforts paying off by providing prospective physical explanations for several phenomena common in the field of fatigue: mean stress sensitivity [11,12], physically short crack behavior [13], environmental effects [7,14] and notch fatigue [6,15,16], to name a few. However, widespread adaptation has yet to be realized, and phenomenological models are still commonly used. ...
... for positive stress ratios, and it should be corrected with a factor (1 − ) for negative stress ratios [12]. The terms th, and , ∈ [1, 2, … , ] denote the additional resistance development and saturation rate, respectively. ...
... However, reflections against the cyclic R-curves measured in [17] indicated that the baseline closure should be even lower (see Section 5.4). The data shows support for the modification of the intrinsic threshold with a factor of 1 − for negative stress ratios, as proposed by Patriarca et al. [12]. Given this input, the predicted KT-diagram could closely reproduce the observed El-Haddad type curve. ...
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... The details of each step performed to define the cyclic R-curve are provided in the Appendix A. The analytical model used to fit the experimental data points, established by Maierhofer et al. [32], is based on Equation (5): The ΔK th defined by Equation (5) is divided into two components: an intrinsic one, ΔK Δa=0 th , and an extrinsic one, ΔK op th . The intrinsic component corresponds to the value of ΔK at zero crack extension and is defined as proposed by Patriarca et al. [57] in Equation (7): ...
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