The stress intensities were not sufficient to grow the crack.
The number of cycles that can be achieved before failure is:
$$ N_{fail} = $$


cycles to failure 
The total number of cycles in the stress history, \(N_{hist}\), is cycles. The number of stress histories that can be repeated before failure is:
$$ X_{hist} = { N_{fail} \over N_{hist} } = $$


history repetitions to failure 
WARNING: The number of history repetitions to failure is small, so the ordering of the stress ranges in the histry may have a significant effect on the results.
Cause of failure:
NOTE: A factor of safety should be applied to the reported cycles to failure to account for any uncertainty in the initial crack size, the applied stresses, and the fracture and fatigue crack growth properties of the material. It is the responsibility of the engineer to determine the appropriate factor of safety to use in design.
The plot below shows the crack size as a function of stress cycles.
See full result details on the other tabs (above).
This section details the crack geometry, material properties, and applied stresses.
Crack Geometry
Stress History
The table below shows the individual stress ranges that make up the stress history. The stress history is run repeatedly until failure.
Cycles 

Tensile Max 
Tensile Min 

Bending Max 
Bending Min 
Total number of cycles in stress history: 
$$ N_{hist} = $$


Equivalent ZerotoTension Stress
The crack progression method of "grow a" was selected for this analysis. In this case an equivalent zerototension stress is calculated based on the stress history, and it is used to calculate crack growth. The peak stress from the history is used to check for failure on each cycle.

Tension 
Bending 

Equivalent zerototension stress:




Peak stress for checking failure:



Note

Fracture Properties
Fatigue Crack Growth Properties
da/dN Curve
Below is a plot of crack growth rate, da/dN, versus \(\Delta K\) for the material used in this analysis. There are several curves shown for varying Rratios. Note that crack growth rate increases with increasing Rratio.
Fracture Toughness vs. Thickness
The fracture toughness is dependent on part thickness. As the thickness increases the fracture toughness decreases until the planestrain fracture toughness, \(K_{1C}\).
The fracture toughness (i.e. critical stress intensity) values for the planestrain condition and for the current part thickness are provided in the table below:
PlaneStrain Fracture Toughness 
K_{1C} = 
Fracture Toughness at Part Thickness 
K_{c} = 
For this analysis, we have elected to use the :
K_{crit} = 

fracture toughness considered in this analysis 
The stress intensities were not sufficient to grow the crack.
The number of cycles that can be achieved before failure is:
$$ N_{fail} = $$


cycles to failure 
The total number of cycles in the stress history, \(N_{hist}\), is cycles. The number of stress histories that can be repeated before failure is:
$$ X_{hist} = { N_{fail} \over N_{hist} } = $$


history repetitions to failure 
WARNING: The number of history repetitions to failure is small, so the ordering of the stress ranges in the histry may have a significant effect on the results.
Cause of failure:
NOTE: A factor of safety should be applied to the reported cycles to failure to account for any uncertainty in the initial crack size, the applied stresses, and the fracture and fatigue crack growth properties of the material. It is the responsibility of the engineer to determine the appropriate factor of safety to use in design.
The final crack size is:
The plot below shows the crack size as a function of stress cycles. Since the stress intensity factor, \(K\), is dependent on crack size, the stress intensity increases as the crack grows. Once the crack reaches the critical size (i.e. the crack has grown to the point that the stress intensity equals the critical stress intensity, \(K_{crit}\), of the material), the part fails catastrophically due to fracture.
The plot below shows the stress intensity factor, \(K\), as a function of stress cycles. As the crack grows, the stress intensity increases until it equals the fracture toughness (critical stress intensity) of the material, after which the part fails catastrophically due to fracture.
The plot below shows the dimensionless geometry factor, \(Y\), as a function of stress cycles.
The table below is an abbreviated sampling of the crack growth results. These results were derived using the methodology described here.
N 
Stress Range # 
a [] 
c [] 
K_{max.a} [] 
K_{max.c} [] 
\(\Delta K_a\) [] 
\(\Delta K_c\) [] 
da/dN [] 
dc/dN [] 
Download Simulation Details to Excel
Download an Excel file to your computer containing the crack growth simulation results.