Progress in the measurement of the cyclic R-curve and its application to fatigue assessment

Highlights

• The crack propagation threshold depends on the crack length.

• A new experimental methodology to determine the R-curve is presented.

• The R-curve is used to predict the endurance limits of micro-notched specimens.

Abstract

The cyclic R-curve describes the resistance of a material to fatigue crack propagation from the short to the long crack regimes and it is therefore an essential ingredient in any fracture mechanics-based fatigue assessment procedure. This work presents different testing procedures employed in the experimental determination of the cyclic R-curve, especially focusing on the comparison with long fatigue crack propagation thresholds obtained by means of the compression precracking load reduction (CPLR) procedure. The tests were performed on the EA4T steel considering different stress ratios. The results show a good reproducibility of the cyclic R-curves at every stress ratio and for any testing procedure. In addition, the cyclic R-curves were used in a fracture mechanics-based assessment to predict the fatigue limits of specimens containing micro-notches.

Introduction

The safe design of engineering components relies on different design philosophies according to how the initiation and evolution of the fatigue damage are quantitatively considered with respect to the safety and reliability level accepted for the component [1]. Under the assumption that most of the engineering components are inherently flawed due to material or fabrication defects [2], [3], [4], a damage tolerant approach based on fracture mechanics is well suited for fatigue life assessment. This approach finds major application in the determination of the residual life and inspection intervals [5] under the assumption of pre-existing flaws detected by nondestructive methods. Note, however, that a fracture mechanics-based approach can be used for the calculation of the total life of a component if small initial defects and short crack propagation are taken into account [6].

The damage tolerance approach can also be adopted in the infinite life regime as the fatigue limit can be interpreted as the non-propagating condition of the largest crack which can be find in a material (or component). This arrest condition depends on the different stages of crack propagation. Microstructurally short cracks arrest at microstructural barriers such as grain boundaries [7], while in the stage of mechanically and physically short cracks the main arrest mechanism is represented by crack closure [8]. While fracture mechanics cannot be applied to predict the fatigue behaviour of microstructurally short cracks, the growth of mechanically short and long cracks can be described by elastic–plastic and linear elastic fracture mechanics, respectively [9]. It is also generally accepted that the time to nucleation and the propagation at the long crack stage give minor contributions to the overall lifetime [10]. Therefore, the understanding and modelling of crack closure is vitally important for the correct and reliable prediction of the fatigue limit conditions of a component.

Under the concept of fatigue crack closure, it is understood that propagation occurs just when a crack is open. From the early pioneering work by Elber [11] several studies demonstrated that mechanical contact of the fracture surfaces may take place even above the zero load level. This leads to the important conclusion that not all the applied $\Delta$K contributes to crack propagation, but just an effective portion of it defined as $\Delta K_{\mathrm{eff}}=K_{\max }-K_{\mathrm{op}}$, where $K_{\max }$ is the maximum stress intensity factor (SIF) in a fatigue load cycle and K${}_{\mathrm{op}}$ the SIF at the crack opening load. The influence of fatigue crack closure on the crack propagation behaviour is significant, especially in the near-threshold regime [8], [12]. The most important mechanisms contributing to crack closure are the plasticity-induced (PICC), the roughness-induced (RICC) and the oxide-induced (OICC). One or the other of these mechanisms is prevalent according to the mechanical properties of the material and the in-service environmental conditions. Recent investigations on the EA4T steel, which is the material considered in the present work, revealed that RICC and OICC, besides PICC, have a prominent effect on the long fatigue crack propagation threshold $\Delta$K${}_{\mathrm{th,LC}}$. In this regard, Pokorny et al. [13] and Vojtek et al. [14] showed that the crack closure function $f$ proposed by Newman and implemented in NASGRO [15] (including plasticity-induced crack closure mechanism only) is not able to sufficiently describe the crack closure in threshold region. Similar mechanisms on the same material were observed by Beretta et al. in case of tests conducted under variable amplitude loading [16]. From the referenced studies, it is then evident that a more refined characterisation of the crack closure effects on the fatigue crack propagation threshold $\Delta$K${}_{\mathrm{th}}$ in the mechanically short to long crack regimes is necessary.

The fatigue crack propagation threshold $\Delta$K${}_{\mathrm{th}}$ can be separated in two main contributions: (i) an intrinsic one, $\Delta$K${}_{\mathrm{th,eff}}$, and (ii) an extrinsic one, $\Delta$K${}_{\mathrm{th,op}}$, which describes the crack-tip shielding mechanisms:

$$\Delta K_{\mathrm{th}}=\Delta K_{\mathrm{th,eff}}+\Delta K_{\mathrm{th,op}}$$

While the intrinsic fatigue crack propagation threshold $\Delta$K${}_{\mathrm{th,eff}}$ depends solely on the elastic material properties (Young’s modulus) and on the magnitude of the Burgers vector ($\Vert \mathbf{b}\Vert$) [17], $\Delta$K${}_{\mathrm{th,op}}$ increases in the mechanically-short crack regime due to contact shielding mechanisms (crack closure) which build up with the crack extension $\Delta$a. The $\Delta$K${}_{\mathrm{th}}$ generally reaches an asymptotic value which corresponds to the long crack threshold SIF range $\Delta$K${}_{\mathrm{th,LC}}$. The crack length dependence of $\Delta$K${}_{\mathrm{th}}$ was documented by several studies [18], [19], [20], [21], [22]. In analogy to static loading, this increase of $\Delta$K${}_{\mathrm{th}}$ with crack extension is named cyclic R-curve, which was introduced by Tanaka et al. [21], [23].

The cyclic R-curve can be used to predict the fatigue limit of components containing small defects like casting porosity, inclusions, corrosion pits [24], or even in special applications such as fretting fatigue [25] and influence of the surface roughness (notch sensitivity) [26]. The most promising application of the cyclic R-curve method is undoubtedly the prediction of the threshold stress, ${\sigma }_{\mathrm{th}}$, as a function of the non-propagating crack length, which goes under the name of Kitagawa–Takahashi (KT)-diagram [21], [27], [28], [29], [30], [31]. In fact, if the KT-diagram can be predicted based on the cyclic R-curve, the extensive fatigue tests on micro-notched specimens needed for the determination of the KT-diagram can be replaced by a single experimental test to obtain a cyclic R-curve. Recently, Maierhofer et al. [32] showed that particular attention should be paid when the KT-diagram is obtained on small artificial notches of finite depth.

There exist several studies in the literature dealing with the experimental determination of the cyclic R-curve [11], [22], [33], [34], [35], [36]. These studies are mostly based on indirect methods, such as the record of the load–deflection characteristic by means of a clip-on-gauge mounted at the mouth of the specimen, or the measure of successive crack-arrest events during crack extension. More recently, a direct methodology was proposed to measure with higher precision the opening stresses, ${\sigma }_{\mathrm{op}}$, by adopting the concept of “crack-tip opening displacements” and “local strain cycles”, in which the strain cycles are measured by Digital Image Correlation (DIC) in proximity of the crack tip [37], [38], [39], [40]. However, the definition of the entire R-curve, along with the experimental techniques and procedures to be adopted to fully describe it, are still key aspects to be fully understood and this study aims particularly to provide new insights on them.

In the present paper, first a comprehensive overview of the basic methods for determining the cyclic R-curve is discussed. The different methods are used in an extensive experimental campaign conducted at Bundesanstalt für Materialforschung und -prüfung (BAM) and Politecnico di Milano (Polimi), devoted to the determination of the cyclic R-curve for the EA4T steel at load ratios R= −2, −1 and 0.05. The results of the different experimental techniques are compared with each other and with a set of fatigue long crack propagation thresholds obtained by compression precracking load reduction (CPLR) in a previous study. The fatigue limits of specimens with artificial defects were determined as well. The obtained R-curves were used in a fracture mechanics-based fatigue assessment to predict the fatigue limits of the artificial defects.