DECLARATION 2 PUBLICATIONS
2.2 Experimental methods
2.2.4 Residual stress and fatigue strength of welded structures
2.2.4.4 Fracture mechanics approach
The fracture mechanics approach is generally used in applications where there is an existing crack, and the method is based on crack growth data. In fracture mechanics, the crack initiation phase is assumed to be negligible and the determined fatigue life is based on the SIF, which accounts for crack size, weld joint geometries and stresses at the tip of the crack. The American Society of Testing and Materials Standard (ASTM) E647 is an international standard used to evaluate fatigue properties of a notched specimen with a fatigue pre-crack under cyclic loading.
Crack size is measured as a function of elapsed fatigue cycles, and resultant data are subjected to numerical analysis to determine the crack growth rate (da/dN) as a function of the stress range (ΔK). The calculation is shown as da/dN(ΔK), which characterises the material’s resistance to stable crack extension under cyclic load. The da/dN versus ΔK relationship is independent on planar geometry, which effectively means that cracks of different magnitudes that are subjected to the same nominal ΔK will advance by equal increments of crack extension per cycle (ASTM E647, 2015).
The fracture mechanics approach is anchored in the modelling of crack behaviour in cracked structures. The method examines design stress, flaw size and material property of fracture toughness as variables in assessing the structural integrity of cracked components. The utility of the fracture mechanics approach lies in understanding the safety thresholds of cracked structures in operation, such that incidents related to production disruption, injuries to humans, and damage to property and plant equipment can be averted. The nature of analysis therefore allows the determination of residual fatigue strength of the structure as a function of crack size, crack growth rate and critical crack size tolerance (Ngiam, 2007).
22 | P a g e Fracture mechanics concepts are grouped into two categories: stress intensity concepts and crack propagation concepts. The notch stress intensity factor (N-SIF) approach uses the notch SIF at the weld toe with zero radius, and crack-tip SIF for the weld root. In the crack propagation approach, the Paris law is used to determine the fatigue life of a propagating crack. Linear elastic fracture mechanics (LEFM) and elastic-plastic fracture mechanics (EPFM) are two main methods in the crack propagation approach. LEFM is often used to estimate the fatigue life of a weld joint where a linear relationship exists between fracture toughness of the material and applied stress.
By contrast, EPFM is used if the relationship is non-linear. The non-fused part of the root is considered to be the initial crack, whereas initial crack depth has to be assumed at the weld toe (Fricke, 2012). The SIF concepts can also be assigned to ENS concepts (Radaj et al., 2009).
The fatigue crack growth (FCG) behaviour can be divided into three main regions, as described below (Caine & Frain, 2016). The three regions are illustrated in Figure 2.3 through the FCG curve.
a. Region I: The growth rate in this region is very slow and is not measurable. Threshold SIF range (ΔKth) is found within this region, and this is the SIF range below which fatigue life is infinite or where crack growth rate (da/dN) is 10-10 m/cycle.
b. Region II: In this region, the curve of FCG rate versus SIF range (da/dN vs. ΔK) is almost linear, and is defined by the Paris equation. Note that C and m are constants of the Paris equation, as shown in Figure 2.3.
c. Region III: Rapid unstable crack growth, which leads to fracture, occurs in this region.
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Figure 2-3: Characteristic curve for fatigue crack growth Source: Cain and Frain, 2016
FCG is difficult to predict in welded structures, which are subjected to multi-axial loads. One of the main reasons for such difficulty is the statistical variations related to the weld parameters.
Parameters such as toe radius and weld bead geometry tend to vary from joint to joint, even if the welding conditions for different joints are deemed identical (Lazzarin et al., 2004). For this reason, the approaches used in the evaluation of fatigue strength for welded joints tend to pick and choose parameters considered to be key for fatigue behaviour within the context of a chosen approach (Lazzarin et al., 2004). Studies have shown that in welded structures, most of the fatigue life is consumed during the crack nucleation stage and subsequent V-notch singularity-controlled growth. Furthermore, in welded joints subject to multi-axial loading, it is not nominal or hotspot stresses that cause the damage but local stresses at the notch of the weld – that is, the root or the toe (Nazzarin et al., 2004). In a fillet weld, fatigue crack usually begins at the weld toe and propagates either into the weld metal or the parent metal, depending on the type of loading. Such cracks are likely to originate from the HAZ or fusion zone of the weld (Al-Mukhtar, 2010). Using high-strength materials can achieve the generic objective of attaining higher stresses using reduced parent material dimensions, but this would not change the fatigue strength. Fatigue strength does not depend on parent metal strength but rather on the geometry of the weld joint (Al-Mukhtar, 2010). The notch SIF approach implies that “the fatigue strength assessment of welded joints failing at the weld root or weld toe is essentially a notch effect problem”
(Meneghetti, 2013). The weld geometry, including weld root and weld toe, is discussed in detail in Chapter 4 below.
Weld root cracks are considered more dangerous than weld toe cracks, because the former are difficult to detect before it is too late. Weld root cracks originate from the root and usually
24 | P a g e propagate through the weld throat into the surface. Only after such propagation do they become visible. Furthermore, stress-relieving processes such as post-weld heat treatment1 are more effective at the weld toe region than at the weld root (Fricke, 2012). Weld roots of fillet and butt welds have been shown to be under compressive residual stresses of magnitudes approaching the material yield strength, for multi-pass welds of mild steel. The residual stress distribution at the weld toe of the multi-pass weld depends on the number of passes, weld penetration and inter-pass time (Fricke, 2012).
Khurshid and Muntaz (2011) compared various standards for joint design in a welded high- strength telescopic beam of a heavy-weight lifting spreader. They also evaluated the effect of weld defects, such as lack of penetration, on fatigue strength of the joint. A combination of 3D numerical analysis and the analytical effective notch stress method (ENS) was used to evaluate the fatigue life of the weld joints. The ENS method is recommended for plate thicknesses above 5 mm, and a fatigue life value (characteristic fatigue strength) of 225 MPa is recommended for steel in fatigue calculations. The notch can be keyhole-shaped or U-shaped, depending on how the weld is prepared. The effect of the shape on the value of the stress has been shown to be negligible. The authors concluded that the ultimate strength of the weld increases with penetration (Khurshid & Mumtaz, 2011).
Khurshid et al. (2017) investigated tube-to-plate welded joints in terms of fatigue resistance to multi-axial stress state and weld root failure analysis. The researchers used local stress evaluation methods. The stress concentration factor due to pure torsion load was Ktt = 2.31, and the fictitious notch radius was 1 mm. Only stress concentration factors at weld roots were considered. All cracks initiated at the weld root and hence weld start/stop had no influence. Two modes of failure were observed; in the first mode the crack propagated through the leg size, then through the throat of the weld. The second mode saw the crack propagate through the weld throat.
Meneghetti (2012) applied FEA to determine the fatigue strength of welded lap joints and cover plate joints. The peak stress method was used for assessment of Mode I and Mode II loading of weld toe and weld root geometries. The peak stress method is a simplified numerical method to estimate the notch SIF parameters. The notches at weld root and weld toe are referred to as V- notches, with angles of 0˚ and 135˚ respectively. Pre-cracked joints (e.g. root gap) are regarded
1Sterjovski et al. (2004), in an analysis of cross-weld properties of quenched and tempered steels, define post-weld heat treatment as “a stress-relieving process whereby residual stresses are reduced by heating between 540 and 590 oC for a set time depending upon plate thickness.”
25 | P a g e as Mode II stress problems. Load-carrying cruciform fillet joints are considered to be Mode I (Meneghetti, 2012)2.
Meneghetti (2013) provided a simplified method to measure Mode III stresses at the weld toe, by correlating the FEA technique with the notch SIF values. Tube-to-flange fillet welded joints subjected to torsional loading were evaluated using LEFM. Similarly, Lu (2002) examined the extent of the influence of WRS on the fatigue life of welded components. Low-cycle fatigue tests in a cantilever setup were conducted. Fatigue cracks occurred at the weld toe in all the experiments, and ratcheting strain was highest at the weld toe. The fatigue life of materials is therefore reduced in the presence of ratcheting3 (Lu, 2002).