Crack Propagation Mechanisms for Creep Fatigue: A Consolidated Explanation of Fundamental Behaviours from Initiation to Failure
Abstract
:1. Introduction
2. Background Literature
2.1. Phases of Crack Growth
2.2. Established Principles in the Literature
- (a)
- (b)
- The strain energy release rate [20,21] determines the crack-growth rate. This mechanism underpins the unstable stage after the threshold of crack initiation. In this stage, increased energy accelerates the increase of crack-growth rate at the beginning phase, which is then retarded due to reduced energy and finally achieves a stable state.
- (c)
- (d)
- The plastic blunting process [24,25,26,27] has asymmetrical effects in the tensile and compressive loading cycles. This mechanism describes crack-growth behaviour in one loading cycle. The tensile loading blunts the crack tip, and the new crack surface is created due to a shearing effect. Then, when the loading is reversed, the surface created under tensile loading remains (crack extension) because of a crushing effect.
- (e)
- (f)
- Diffusion creep [12,13] provides a mechanism that leads to grain elongation and then further crack opening. In addition, since atoms diffuse from a high- to a low-concentration region, more vacancies are generated and converged at the crack tip, where highly localised stress is presented, which provides a more favourable situation for creep damage.
- (g)
- Existing precipitates [31] cause fatigue resistance. The mechanism is mainly that precipitates are the obstacle to dislocation, and hence restrain the process of crack propagation.
- (h)
- Crack deflection (change of direction) [32] preferentially occurs at the grain boundary. This is determined by the twist angle and the tile angle.
- (i)
- (j)
- A region with a high density of micro-cracks is particularly weak, and supports crack-branching activities [33].
- (k)
- The slip bands within grains [34] may cause the crack to re-direct within grains.
- (l)
- The plastic energy [23] available exceeds the need for producing the new crack surface. The excess energy is applied to form voids, and thus further worsens creep-fatigue resistance.
2.3. Gaps in the Body of Knowledge
3. Approach
4. Results
4.1. New Propositions
- A
- That energy dynamics explain the crack initiation and the following unstable phase, and is based on a liberation of energy due to coalescence of dislocations. In general, when the internal energy stored in the structure due to cyclic loading arrives at a critical value, the barrier to initiate the crack is overwhelmed. After this, the released energy is gradually consumed to produce new crack surfaces at an accelerated crack growth rate.
- B
- That grain-mismatch occurs due to grain elongation under the tensile loading, resulting in relative movement between two neighbouring grains. Then, the shear stress along the grain boundary is increased and a weaker region along the grain boundary is created. This results in a mismatch band at the grain boundary. This widens the crack body and enhances its growth.
- C
- That bonding crushing effects exist at the finer scale. During the process of compression, the atomic bonds, which are distorted and rearranged in the tensile phase, may be further damaged and become potential failure sites for next loading cycle. This process is irreversible, since the atoms cannot return to their original position under the compressional loading.
- D
- That a crack net is caused by the aggregation of micro-cracks. This crack net probes a larger volume of material for weaknesses, and then promotes the main crack.
- E
- That irregular configuration of the grain boundary causes stress/strain pile up at the grain boundary, and then results in a large driving force for extending the crack tip into the neighbouring grain.
- F
- That the primary mechanism for failure in the creep-fatigue loading regime is crack growth by mechanisms of crack blunting (including shearing and crushing); hence, fatigue effects.
- G
- That the supporting mechanisms that augment the extent of damage are grain elongation and diffusion; hence, creep effects.
4.2. Conceptual Framework of Temporal Development of Crack-Growth for Creep Fatigue
4.2.1. Stage I: Crack Initiation
4.2.2. Stage II: Crack Propagation
4.2.2.1. Crack Tip within a Grain
4.2.2.2. Crack Tip at Grain Boundary or Triple Point
4.2.2.3. Crack Tip through Grain Boundary
4.2.3. Stage III: Structural Failure
5. Discussion
5.1. Summary of the Crack Growth Process and Mechanisms
5.2. Original Contributions
5.3. Implications for Practitioners
5.4. Limitations
5.5. Implications for Further Research
- (1)
- The crack-growth behaviours at the grain boundary when crack tip at/through the grain boundary. The question is that it is difficult and complex to empirically examine and investigate the phenomena at the grain boundary since it will be difficult to dynamically capture those moments when the crack tip arrives at the grain boundary. To catch this microstructural behaviour, a new experimental method may also need to be developed.
- (2)
- The grain-mismatch behaviour due to grain elongation under the tensile loading. It is valuable to explore the shape change of grains under tensile loading, and observe the relative movements and investigate the interfacial phenomena between two neighbouring grains. This research may also be extended to the situation of compressional loading.
- (3)
- The bonding crushing effects during the process of compression ahead of the crack. This is a call for an atomic-level investigation, e.g., using atomic force microscopy. Existing approaches have been focussed on statically describing the force-distance relation and force field between two neighbouring bonds. This provides valuable information on the local material properties [59,60,61]. However, the dynamical process (such as the time-depended force/distance variances and the trace of atomic movements) under a cyclic or constant loading have not been addressed. In addition, it may also be valuable to explore both the situations of tensile and compressional loadings.
- (4)
- The stress/strain pile-up at the grain boundary because of the irregular configuration of the grain boundary. This is the question of investigating the dislocation pile-up [62] and measuring the stress field at the grain boundary [47]. The future research may start from the existing theories and methods, and then go further to evaluate the configuration-based effects at the grain boundary. In addition, finite element analysis may also be involved to investigate the stress/strain distributions and the shape distortion at the simulative grain boundaries.
- (5)
- Numerical modelling and its experimental validation. This could be done at several levels. At a high level of abstraction, there are already formulations for describing the failure process. For example, Paris’s law [11] gives the crack growth in one cycle based on the stress intensity factor, the Arrhenius equation [63,64] presents the creep behaviour at the steady stage based on diffusion creep, and the conventional loading-life equations (the Basquin [65,66] equation and Coffin-Manson [67,68] equation) model life based on empirical data. At the level of detail providing in this paper, as represented in Figure 19 and Figure 20, the crack-growth process is graphically described in the microstructural level.
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Liu, D.; Pons, D.J. Crack Propagation Mechanisms for Creep Fatigue: A Consolidated Explanation of Fundamental Behaviours from Initiation to Failure. Metals 2018, 8, 623. https://doi.org/10.3390/met8080623
Liu D, Pons DJ. Crack Propagation Mechanisms for Creep Fatigue: A Consolidated Explanation of Fundamental Behaviours from Initiation to Failure. Metals. 2018; 8(8):623. https://doi.org/10.3390/met8080623
Chicago/Turabian StyleLiu, Dan, and Dirk John Pons. 2018. "Crack Propagation Mechanisms for Creep Fatigue: A Consolidated Explanation of Fundamental Behaviours from Initiation to Failure" Metals 8, no. 8: 623. https://doi.org/10.3390/met8080623