Vextec Learning Center


VEXTEC has authored many papers on our technology and its numerous applications in scientific and engineering journals.  For a listing of our papers click here.

Below we have provided white papers on details of out methods and present various validations studies.  If you have any questions or would like more information on any of the papers below, please contact us.


Here are some terms related to lifing. This section is aimed at those who are unfamiliar with them, therefore we are giving pretty basic explanations without a lot of formulas.


Most commonly used metals are isotropic, which means the material properties are the same in all directions. They are composed of many individual grains, which are non-isotropic. As long as these grains are randomly oriented, the metal will be isotropic.

Grain Boundary

A grain boundary is the region between grains.

Single Crystal

Some damage mechanisms target the grain boundaries. To make longer lasting components, the molten metal is sometimes cooled very slowly so that only one large crystal is formed. This eliminates the grain boundaries altogether. This is expensive, so it is only done on high value components. One common application of single crystal components is turbine blades in gas turbine engines, which are exposed to high stresses and high temperatures.


Fatigue is the damage mechanism that is responsible for most engineering failures. It is caused by loading that is applied and removed. Each application and removal is called a “Cycle”. If the load is sufficiently high and enough cycles are applied, a crack will initiate. Once the crack initiates, it will propagate a small amount for each cycle until it fractures.

Mean Stress / Alternating Stress

Mean stress is the average stress during the application of a cycle. Let’s say we have a component that is cycled between a min stress of 20 KSI and a max stress of 120 KSI. The mean stress is 70 KSI ( [20 + 120] /2 ). The alternating stress is how much the stress varies (plus and minus) from the mean stress during the application of a cycle. It is equal to half the stress range ( [120 – 20] / 2 ) or 50 KSI in this case.

R Ratio

In fatigue we often talk about R Ratio, which is the ratio of the min stress to the max stress. If we have a component that is cycled between 0 and 100 KSI, the R ratio is ( 0 / 100 ) or 0. This is often referred to as “Zero to max” loading. If we cycle between stresses of -50 and 50, the R ratio is ( -50 / 50 ) or -1. This is often referred to as “Fully reversed” loading.

Fracture Mechanics

Fracture Mechanics is the study of crack propagation. Once a crack has initiated, we want to know how fast it will grow.

Stress Intensity Factor

The stress intensity factor (designated as “K” in formulas) defines the stress field in the region around the crack tip. It is a crucial parameter in fracture mechanics. With it we can determine how fast a crack will grow and how large the crack will be when it suddenly fractures. You may remember spending a lot of time trying figure out what “X” was in algebra class. Fracture mechanics guys are always trying to determine K.

Fracture Toughness

Fracture Toughness is the stress intensity factor at which a crack essentialy causes instant failure. This is a material property which varies with temperature.

Paris Law

The Paris Law relates the crack growth per cycle (designated “da/dn”) to the stress intensity factor range.

Threshold Stress Intensity Factor Range

If the stress intensity factor range is small enough, the crack will not grow at all. This is the threshold stress intensity factor range.