A New Crack Initiation Life Prediction Method for Arbitrary Multiaxial Loading Considering Mean Stress Effect.

Applicability of the local strain approach for crack initiation life prediction of notched components under multiaxial service loading is investigated. The necessary tools in multiaxial fatigue - analyses of loading histories and notch stress-strain, deformation and damage theory - are described, and current limitations outlined. Feasibilities are illustrated by examples.

Local Strain Approach in Multiaxial Fatigue - Feasibilities and Current Limitations -

Shortly before final failure or in case of accident or misuse components are subjected to extremely large deformations, whereas under normal LCF conditions the strains normally do not exceed ±2%. In the present paper constitutive equations in connection with the specially developed FEM code INDEED are presented, which enable the evaluation of the stresses and strains at every point of extremely large multiaxially deformed components. It is also indicated which modifications of this special FEM code become necessary if it is applied to LCF conditions. The multi-yield surface model as proposed by Mroz can be used and is already included in the FEMFAT program system. The possibilities to perform fatigue life calculations are also briefly discussed.

Constitutive Equations for Elastic-Plastic Material Behaviour Under Extremely High Multiaxial Loads and Fatigue Loads

This research work involved the prediction of the fatigue life of an automotive rear
suspension twistbeam assembly fitted to a vehicle travelling over a customer correlated
durability route. This was achieved by making use of the integrated concepts of scaling and
superposition of linear static finite element analysis being driven by experimental load data
- the so called 'quasi-static time domain' approach. A study of the free body diagram of the
twistbeam resulted in an indeterminate load set of some 24 components, with experimental
data indicating that a state of static unbalance existed. Subsequent to developing a
matrix-based generalised method ofload cell calibration to confum the foregoing, a modal
technique was developed to partition the experimental data into a static load set, causing
elastic deformations, and a rigid load set, imparting rigid body accelerations. The
semi-independent characteristics of the twistbeam necessitated the coupling of large
structural displacements with inertia relief. This required extensive modifications to the
current techniques and led to the development and use of a three dimensional functional
response matrix in place of the conventional two dimensional one. Recommendations
concerning appropriate finite element boundary conditions were also formulated to handle
these effects. Finally, the limitations of the uniaxial fatigue model were revealed under the
application of a set of tools for analysing the biaxiality and mobility of the maximum absolute
principal stress.

Using experimental loads with finite element analysis for durability predictions

In Low Cycle Fatigue two variables are usually applied to describe the state of a material : 


The damage variable D, 0≤D≤DF, defining the damage of the material, often without any detailed physical explanation. DF is the damage variable at fracture, DF≤1.0.


The number of cycles N. NF is the number of cycles to fracture for a given stress range ∆σ or strain range ∆e. Manson and Coffin gave for a strain controlled test the relation 

$${{\text{N}}_{\text{F}}}\text{ }\Delta {{\varepsilon }^{\beta }}=\text{const}\text{., 1}\text{.5}\le \beta \le \text{2}\text{.0}\text{.}$$

(1)





see e.g. the review by Manson and Halford, [1].

Some Remarks to the Application of Damage Mechanics to Low Cycle Fatigue

LCF-components exhibit quite often complicated distributions of stresses and strains and the loading conditions may be complicated, as well. In the present paper a new finite element based fatigue analysis concept is presented, which includes a (MROZ-type-) material model and a newly developed incremental damage evaluation procedure, which is based on plastic work. This evaluation procedure can be applied to arbitrary in-phase and out-of-phase conditions. An example of the practical application of the procedure is given.

Advanced Fem-Based Fatigue Analysis (Femfat) For Arbitrary Multiaxial Elastic Plastic Loading Conditions

In order to minimize the expenses of the development of engineering components and to reduce the risk of their operation, reliable fatigue life prediction methods have to be available in the design stage. Presently two groups of methods can be distinguished which explicitly account for the local stresses/strains in the fatigue critical areas: the so-called notch analysis concepts or "local approaches," and new developments which are based on finite element methods (FEM). In the first part of the paper typical areas in application of the notch analysis methods and some aspects of their further development are described. The significance of the short crack stage is briefly characterized from a physical and an engineering point of view. In the second part the present state in the development of a new three-dimensional elastic-plastic FEM-based fatigue analysis concept, FEMFAT, is described. FEMFAT uses a material model according to MrOz's proposal, and the fatigue damage is calculated on the basis of the plastic work as performed at the fatigue critical locations of components. A calculation scheme for the damage increments under arbitrary out-of-phase loading based on uniaxial data is proposed. Two examples of the application of FEMFAT are given.

H. Peeken

Papers

Advanced Fem-Based Fatigue Analysis (Femfat) For Arbitrary Multiaxial Elastic Plastic Loading Conditions

Some Contributions to the Further Development of Low Cycle Fatigue Life Analysis Concepts for Notched Components under Variable Amplitude Loading