Domain

Explanation

Fracture?

• The word "fracture" are of the following 2 aspects:

1. Act: to fracture is to damage something to dislodge a portion of it, but not totally destroying it, whether accidental or otherwise à e.g. bone fracture
2. Process: cultivated focused observations & understanding of fracture occurrences, initiation, propagation, cause-effects & interactions; i.e. what actually happens before, during & after fracture of an object-of-interest

• In engineering, fracture is the cracking, tearing, shearing & dislocating of originally intact structures or components or connections
• Hence,
• The process of fracture is what matters to engineers

Fracture as a form of failure

• Structures are increasingly important & critical to public safety in general & private applications in particular
• For to structures to fail or collapse is akin to the "sky falling down" to some
• Thus, it is not surprising for engineers to be especially sensitive towards failures, whether local or global
• Hence, we see engineers engaging in safety factors, critical limits or states, reliability robustness, prevention & attenuation of processes, conditions & environments that are proved or might of proximate possibility of occurrence
• Failure, it seems, is a definite bane, the tombstone of what it means to engineer à to engineer is to arrest failure is to avert disasters
• Failure has the following 8 attributes:

1. Structure: the constrained domain where the failure-in-question is limited to à e.g. size, geometry, degree of heterogeneity & restraints w.r.t. mechanics (nonlinearity, plasticity), thermodynamics, chemistry, etc.
2. Environment: all endogenous external influencing factors à e.g. loading distribution & configuration (magnitude, direction, plane, rate)
3. History: current failure is influenced by previous configurations & influences, giving rise to pre-existing circumstances
4. Scale: local, regional or global
5. Connectivity: propagation through contacts, connections & links
6. Root: conditions favourable to creating, initiating or growing failures
7. Mode: sequence of failure process from its roots to its consequences, determined by intense misbalance of resistance & disturbance
8. Consequence: conditions arising from the failure itself, possibly enabling balance with structural re-configuration

• If a structure cannot continue in its intended form to serve its intended purpose for its intended environment & period, then failure can be said to occur
• As such,
• Fracture is one form of failure, but failure has many other non-fracture forms
• Hence, fracture inherits all the 8 attributes of failure

Engineering fractures

• Engineering fractures need the understand of fracture roots
• Imperfection always exists: No two elements are the same
• Hence, defects would always be present & in the following 3 types:

1. Active defects: either initiate or propagate fracture cracks
2. Dead defects: no influence whatever on fracture
3. Dormant or benign defects: poses no threat of fracture, but may become active or dead, depending on circumstances of 8 failure attributes

• The defects must be appropriately engineered
• In addition, material failures in mechanics can be:

1. Ductile failures: large deformation, large plasticity, high toughness materials à nonlinear fracture mechanics à significant crack tip plasticity, initially stable crack growth before instability à controlled by holding applied J-integral
2. Brittle failures: small deformation, elasticity with little plasticity, low toughness materials à well-described by linear fracture mechanics à sudden unstable fracture, a single fracture toughness value is sufficient

• Instability during ductile fracture occurs by:

1. Onset of cleavage fracture after stable crack growth
2. Plastic instability or collapse
3. Rapid rate of increase in applied crack tip parameter J or K

• Crack growth occurs when:

1. Crack tip parameter > critical crack resistance capacity
2. Detrimental configurations of size, geometry & loading characteristics
3. Interaction from high loading rates: some leakage into kinetic energy of cracks, lesser for fracture propagation; sensitivity of fracture resistance to loading rates & complications from reflected stress/strain waves

• Constraint effects & microscopic aspects into fracture mechanics: variable & higher-order terms of crack parameters away from crack tips & in the region of damage leading to cracks
• Creep-fatigue crack growth under elevated temperature: under sustained &/or cyclic loading portion of the cycles à predict crack growth rates

Fracture mechanics

• Fracture mechanics is the analytical framework to predict potential for fracture to achieve:

1. Predict crack growth
2. Fracture behaviour
3. Loading: applied stress magnitude & distribution
4. Resistance: of fracture & crack growth of the material
5. Defects: size, location & geometry
6. Influence of service environment

• Fracture mechanics can be classified into:

1. Linear elastic fracture mechanics LEFM: linear elastic stress-strain behaviour, little plasticity, constant single global characteristics; stress intensity parameter K à brittle failures in aerospace
2. Elasto-plastic fracture mechanics EPFM: nonlinearity, large-scale plasticity, J-integral à ductile failures in construction, power generation, chemical & biomedical industries
3. Time-dependent fracture mechanics TDFM: high loading rates, crack tip stresses influenced by shear waves & kinetic energy considerations; time-dependent creep & fatigue; C-integral à creep-fatigue failures in mechanical industries

• Fracture studies can be grouped as global & local fracture mechanisms
• Global fracture mechanics:

1. Characteristics of global structure: useful for surrounding regions away from crack tip of high plasticity, stresses & strains

• Local fracture mechanics:

1. Process zone: microscopic zone very near to crack tip
2. Intergranular cracks: along grain boundaries
3. Transgranular cracks: through & crack grains
4. Mechanisms: cleavage fracture, ductile fracture, brittle fracture, intergranular or transgranular fractures

• Suggested preliminary knowledge prior to failure or forensic investigations:

1. Mathematics: advanced vector-tensor notations, transformations (line integral, Green’s theorem & Gauss theorem)
2. Materials science & engineering: characterization, testing & analysis of materials & substructures à constitutive (stress-strain), properties, attributes
3. Structural analysis: load & deformation behaviours due to interactions of the external disturbances with internal resistance capacities w.r.t. restraints, energy balance, stability, formulations & numerical implementations
4. Experimental analysis: reliable experimentation, tolerable understanding & derivation of results for observations, derivations, verifications & identifications

LEFM

• Stress intensity parameter, K
• Assumption: insignificant plastic deformations
• Strengths:

1. Success on high strength, low toughness materials, especially in aerospace applications
2. Brittle failures: strictly within linearly elastic range à high strength, low-deformation, low toughness materials such aluminum alloys
3. Applicable for global region away from crack tip
4. Unique, global crack tip parameter: stress intensity parameter, K for dominantly elastic conditions
5. K uniquely characterise crack tip stress field in the process zone, which is large in comparison to the region (where microscopic scale damage develops) à in other words, as if like linearization by neglecting higher order terms & thus, applicable only to small displacements
6. K unique for size & shape of the crack tip plastic zone à required conditions: (1) K-dominance; (2) crack tip regions experience the same levels of constraint
7. During crack extension, K unique for rate of release of strain energy à (1) supply required energy for plastic deformation; (2) create new surfaces after fracture

• Limitations:

1. Not applicable for near crack tip: of high plasticity & nonlinearity
2. Neglect higher order terms in expansion: only first-order terms are used
3. Not accurate for highly heterogeneous materials: due to derivation of general, average global fracture parameters
4. Not for ductile failures: large-scale plasticity & nonlinearity à low strength, large-deformation, high toughness materials

EPFM

• Rice’s J-integral

1. Characterise amplitude of crack tip stress fields
2. Size requirements are met
3. Amount of crack extension limited
4. Analytical, numerical & experimental estimations of J-integral

• Strengths:

1. Address the deficiencies of LEFM, while retaining all strengths of LEFM
2. Particularly suitable for ductile materials & near crack tip regions, inclusive catenary actions

• Limitations: static conditions without rate-dependency under very low or quasi-static loadings

TDFM

• D J-integral & C^*-integral
• Strengths: address deficiencies of EFPM, especially under creep (steady loading under elevated temperatures) & fatigue (cyclic loading oscillations)
• Limitations: restricted to either global fracture mechanism, or local fracture mechanism, but not both (which is the realistic situation)
• Required in future: a bridge between well-established global & local fracture mechanisms in order to link up the two
• Criteria to satisfy: meets all basic fundamentals of each extreme - global & local fractures; as well as transition between local & global w.r.t. or dependent on the material, size, geometry, loading & interaction configurations

Applications

• Major aspects:

1. Integrity assessment of structures & components
2. Material & process selection
3. Prediction of design life or remaining life
4. Inspection criterion & interval determination
5. Failure analysis

• Fracture mechanics methodology:

1. Problem statement
2. Material properties
3. Crack models
4. Fracture mechanics analysis
5. Findings

• Possible future applications:

1. Earthquake rupture mechanics: missing link in earthquake designs, where earthquake prediction & prevention understanding is still in a state-of-research, i.e. not known
2. Geological engineering: aid in the exploitation of natural resources in extremes environmental conditions
3. Construction defects
4. Nanostructured materials
5. Biomedical implants & bionics: better biocompatibility & reliability of life-saving biomedical implants & life-enabling bionic applications

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• Types: Polymeric materials, polymer, ceramics, metal alloys