Crack Propagation Simulation of Variable Amplitude Load Fatigue: Case Study 1

Author: FAConle Created: Feb 07 2014 Updated: May 2014


A crack propagation computer program that accounts for material memory
and applies the BS7910-2005 design guidelines has been applied to the variable
amplitude loading results on edge cracked plates presented in paper:

M.Luke, I.Varfolomeev, K. Luetkepohl, A. Esderts, "Fracture mechanics
assessment of railway axles: Experimental characterization and computation,"
Engineering Failure Analysis 17 (2010) 617-623

Materials and Specimens:

The work by Luke et al used two types of railway materials: the axle steel 25CrMo4
and the high strength steel 34CrNiMo6 with 0.2% offset yield strengths of
550 mpa and 950 mpa repectively. The specimens used for generating baseline da/dN
curves and for the variable amplitude tests were single edge cracked (3mm) plates of
width 24 mm and thicknes 10 mm. Curves for da/dN baseline data were generated with
tests using load ratios of R=-1.0 and R=0.1 for both materials.
For the present simulation study a digital approximation of the R=-1.0 da/dN data
was fitted visually to the reported experimental data as shown if figure 1
and 2. (black points)

Fig. 1: Fitted da/dN points of 25CrMo4 Steel.

Fig. 2: Fitted da/dN points of 34CrNiMo6 Steel.

For the crack initiation part of the simulation four data sets were merged into
one file (Raw available here). and the "fitted" stress-strain-life curve (Fitted file available here)
was then used to predict crack initiation life for an uncracked sample subjected
to the same nominal stress history. The original paper by Luke et al did not
report any initiation tests, but the simulations are presented below to serve as
a comparison alongside the crack propagation predictions.

Load History:

As presented in the Luke et al paper, the load history consists of five
sub-blocks. Each sub-block has a different fully reversed stress and a
number of specified cycles per sub-block.

The sub-blocks are divided into sub-block segments and the arrangement of
the segments is described in the text file here.

A program was used to convert the segment descriptors into a half cycle by
half cycle sequence. The program is available here:


Click to enlarge

A peak by peak history of membrane (Pm) and bending (Pb=0.0) are available
in the file

c100histPm.txt (1 Mb)

In the history the "100" value for the peak is proportional to the test reference stress
for sub-block 1 (the lowest stress sub-block). The arrangement of the sub-blocks and
their maxima stresses is a bit complicated and the reader is referred to the
paper by Luke et al for a full explanation.

Simulation Programs:

An outline of the program logic that underlies the crack propagation program is
available at the following web locations:

The edge cracked plate simulation program version is available here:

Other run-time files are:


The results, similar to the predictions published by Luke et al, are:

34CrNiMo6 Steel:

 Delta S= 200 mpa  :  Fracture at   77688 cycles  @ a= 3.97 mm   0.027 sec cpu

 Delta S= 120 mpa  :  Fracture at  701701 cycles  @ a= 6.70 mm   0.126 sec cpu

25CrMo4 Steel:
  Delta S= 200 mpa :  Fracture at   77688 cycles  @ a= 3.72 mm   0.021 sec cpu

  Delta S= 120 mpa :  Fracture at  987701 cycles  @ a= 6.49 mm   0.152 sec cpu

  (See Luke et al  for experimental  crack length vs. cycles data)

The higher stress level simulations are within a factor of two of experimental lives, while
the lower stress level simulation predictions are within a factor of 3 of the
experimental lives observed by Luke et al to be approximately 1.3 million cycles.

Damage computation was made for each half cycle. Both materials simulated
at Delta S= 200 mpa failed at the first large +-280 mpa cycle in the 4th
history repetition.

It should be noted that the simulation program corrects for material memory
but it does not presently compensate for overloads. The mean stress correction
and the crack closure code segments have been turned off, resulting in a simulation
that follows BS7910-2005. For this particular load history material memory compensation
is not expected to alter the results greatly.

The simulation program generates a report for each test and the pdf files are
available here: