Table 1 Comparison of physics based methods

Life prediction based on stress [10, 30, 31]

Simple and easy to analyze;

Low accuracy;

The initial design estimation;

Parameters required are few and easy to get;

Poor adaptability for the parameters depend on geometry and loading forms, etc.;

Long-life components such as the spring shaft and gears and other high-strength materials;

Rich data sources with accumulated experience can be obtained.

Unable to analyze the gap effect without considering crack.

Whole-life analysis combined with linear elastic fracture mechanics.

Life prediction based on strain [32, 33]

Direct access to the strain parameters by means of measurement;

Complex calculations;

Fatigue test with strain as control condition;

Able to conduct notched fatigue analysis;

Insufficient gap analysis;

Situation of high temperature, large strain and high stress concentration;

Able to judge the impact of the loads order;

Only the crack initiation is considered.

Components with less load cycles, large plasticity, such as low-strength structural steel;

Able to express the cyclic stress–strain response;

Whole-life analysis combined with linear elastic fracture mechanics.

Conducive to fatigue–creep mixture analysis.

Life prediction based on accumulative fatigue damage [33, 34]

The impact of actual magnitude and the order of loads has been taken into consideration;

Only parts of the influence factors have been considered, failed to conduct a comprehensive analysis of the complexity of life prediction;

The material and mechanical parts subjected to cyclic loading;

Matured and widely used.

Narrow scope of application.

More used in engineering.

Life prediction based on fracture mechanics [17, 33, 35]

The mechanism of the crack propagation can be physics interpreted since the crack propagation is taken into consideration;

Difficult to measure and estimate the initial crack size; no research on the initial crack;

Large and important parts and structures, such as aircraft, nuclear reactors;

Able to control the initial damage, the examination period and working loads, etc. to ensure safety.

Uneasy to calculate the stress intensity factor of the components with complex geometry;

Metal materials with metallurgical defects in themselves and components with pores, slag and weld defects created in welding.

Elastic–plastic fracture mechanics is used since linear-elastic fracture mechanics can hardly meet requirements in general cases.

Life prediction based on damage mechanics [33, 36]

Good agreement with the fatigue mechanism in experimental observations;

Complex calculation and analysis;

Insufficient research on damage mechanics of some materials and components.

Only applied for some metal materials, composite materials and concrete materials

Easy to measure the fatigue damage.

Life prediction based on energy [26, 29, 32]

Unified representation, and strong universality;

Insufficient research;

Composite panels of composite tissue, such as alloy laminate, coating structure;

Allowed to take the mean stress and the impact of multi-directional load into account.

Few applications.

Piezoelectric material and the composites.