# Multiple Scaled Experimentation in Fatigue Crack Growth: Finite Similitude Theory

• Osagie Akhigbe-Midu

Student thesis: Phd

### Abstract

A high percentage of all structure or products failures can be attributed to fatigue and fracture. In analysing the behaviour of cracked components, the existence of size effects remains a problem in the prediction of the full-scale fatigue response of structures using sub scale models. The smaller models appear stronger exhibiting a higher fatigue life than the prototype. Thus, fatigue tests performed in the laboratory using small specimens cannot be reliably used to predict the fatigue behaviour of a larger structure e.g., bridges, aircrafts, boiler pressure vessels etc. Experimental testing for fracture mechanics can be expensive, especially if the structure/component is large or if the material used is expensive. Scaled modelling is a possible method of decreasing experimental costs. Scaling techniques such as dimensional analysis are currently used in fracture mechanics and fatigue to design meaningful scaled experiments; however, it has several limitations primarily in its inability to account for size effects. This necessitates the need for a new method; first order finite similitude theory which can offer a cost-effective solution and more reliable results. A novel mathematical equation has been formulated in this thesis that establishes a precise analytical relationship between fatigue life and scale providing new insights into scaled experimentation in fatigue. Unlike dimensional analysis, the theory of finite similitude connects information across scales and links more than one scaled experiment. It is shown for the first time that conducting two scaled experiments is the correct scaling approach for the analysis of fatigue as the geometric size effects that are present in both mode I and mixed mode (mode I/II) fatigue crack growth with a change of scale are eliminated. Several case studies commonly employed in laboratory fatigue tests are examined numerically such as the ASTM E647 standard specimens and compact tension shear specimen. Practical case studies such as pressure vessel, pipe under pressure load, welded t-joint, pin loaded lug among others are also investigated numerically. The relevant experimental data and finite element models demonstrate clearly that the new rules for predicting fatigue life and crack growth rate provide good accuracy. Errors in lifecycle and stress intensity factor predictions ranged between 0.1-9% whereas the crack path and shape were predicted with 99% accuracy. The hitherto difficult task of achieving complete similarity in Paris law is proven possible in this thesis by performing an extra scaled experiment as Paris law constants C and m are predicted with up to 99.9% accuracy. The promising results demonstrated in this thesis confirm the value of employing this scaling approach to scaled fatigue experimentation in any industrial setting that employs a damage tolerant design approach.
Date of Award 1 Aug 2023 English The University of Manchester Keith Davey (Supervisor) & Rooholamin Darvizeh (Supervisor)

### Keywords

• Scaled fatigue testing
• Structural integrity
• Finite similitude
• Damage tolerance
• Fracture mechanics
• Size effects
• Fatigue
• Scaling

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