# We give you the big picture…

Polaritek’s innovative measurement technique is able to rapidly generate full-field stress maps of samples using non-contact optical methods. This is unique in that competing technologies are only able to measure the stress at a single point (often slowly) or conversely are only able to measure the overall global stress. When a part is manufactured or otherwise processed, internal mechanical stresses are generally imparted and these stresses are known as residual stresses. Characterization of residual stresses is a key step when attempting to predict the lifetime performance and failure mode of a part. By utilizing Polaritek stress maps, users can quickly realize the stress magnitude and variations across a part and check the stresses at critical locations. This powerful technique can be applied to many materials such as plastics, glass, sapphire and crystalline silicon among others.

To better understand this technique, first examine the basic system arrangement shown below in Figure 1. In essence, various states of polarized light are transmitted through the measurement sample and imaged by a digital camera. This light interacts with the measurement sample depending upon the polarization state of the light and the internal stress in the sample. As a result of this interaction, interference fringes are formed. A computer with powerful image processing algorithms translates this raw image data into full-field stress maps using the Stress-Optic Law.

The Stress-Optic Law states that the magnitude of stress is proportional to the fringe order, as suggested by Figure 2. The fringe order at each point in the measurement sample is determined by counting the number of full and partial fringes visible in the camera images. It is worth noting that in many applications the total fringe order is often much less than one fringe. With proper calibration, a residual stress value can be calculated from the fringe order. More specifically, this stress is known as the *maximum shear stress*.

Although the expression “stress” is generally understood to mean the internal forces attempting to deform a part, it is important to realize that each element inside a sample is actually subject to multiple stress components of which the maximum shear stress is only one component. In fact, there are both *normal stresses* and *shear stresses*. Figure 3 presents an example small element inside the measurement sample, which is subject to normal stresses σ_{x} and σ_{y} acting normal to the faces of the element in the x- and y-direction, respectively. These normal stresses may be either tensile or compressive. There is also a shear stress, τ_{xy}, which acts parallel to faces of the element. Since the orientation of this element is arbitrary, it could rotated to any angle and the resulting stress components could be recalculated for each orientation. In fact, the element can be rotated to a certain angle which maximizes one of the normal stresses and minimizes the other. In this orientation, the normal stresses are now known as the *principal stresses*, σ_{1} and σ_{2}. Rotating the element an additional 45 degrees will instead maximize the shear stress, which is then known as the *maximum shear stress*, τ_{max}.

In some situations, for example when examining ductile materials, the maximum shear stress is useful as the basis for a failure criterion. However, in other situations such as fracture of a brittle material, the normal stresses (typically oriented along crystallographic directions) are a key source of failure. Tensile normal stresses lead to crack formation and propagation.

The Stress-Optic Law provides only the maximum shear stress. Consequently, the normal stress maps must be calculated in a post-processing step. Fortunately, there is a simple relationship between the principal stresses and the maximum shear stress. This relationship, described in Figure 4, shows that the maximum shear stress is related to the *difference* in the principal stresses. If the principal stresses are known, it is a trivial matter to calculate the maximum shear stress. The present problem of solving for the principal stresses when only the maximum shear stress is known, however, presents a far more formidable challenge. Fortunately Polaritek has developed and patented novel “stress separation” techniques which are able to overcome this challenge and generate full-field stress maps as shown in Figure 5.

Often, residual stresses are characterized with the aim to optimize a manufacturing process by minimizing residual stresses. This requires comparing the stress maps of samples processed in one method to another. Some competing technologies are only able to measure the maximum shear stress. However, if only the maximum shear stress is considered, the results may be unclear. Consider a scenario where processing method A produces a similar maximum shear stress to method B. Since the maximum shear stress depends *only on the difference* between the two principal stresses, it is entirely possible that the principal stresses (and thus the normal stresses) are each either *lower, the same* *or higher* in method A than method B! This is hardly a satisfactory characterization. Therefore, whenever possible, it is always advantageous to reference both the maximum shear stress maps as well as the normal stress maps in order to fully characterize the residual stresses in a measurement sample.

## Let’s discuss what’s currently out there and how we surpass the competition…

Stress measurement systems from Polaritek Systems are:

- Non-destructive
- Non-contact
- Through-thickness
- Rapid (<a few seconds measurement time)
- Able to provide full-field stress maps of local variation
- Able to separate normal stresses

Although there are other stress measurement techniques on the market, no existing technology is able to measure the full 3-D stress field inside a part. While other techniques may seemingly offer advantages in some arenas, they are, overall, unfit for the purpose of quality control and process control in a manufacturing environment due to various shortcomings. These shortcomings can be organized into a few general areas:

- Measurement Time: In a production environment, measurement time is critical. Waiting 30 minutes or more to perform a quality test can mean hundreds or, possibly, thousands of defective product may have been manufactured in that brief period of time. Even in an offline research setting, faster measurement time means more samples can be measured more quickly which presents an obvious advantage. In comparison, Polaritek techniques require only a few seconds or less.
- Surface Stress: Measurement techniques which are unable to penetrate the full sample thickness are only able to provide a measurement of surface stress. Research has shown that surface residual stresses are not representative of either the processes by which they were produced, or the stresses below the surface.
^{[1]}Measurements provided by Polaritek sum stresses through the entire thickness of the measurement sample and are not restricted only to the stresses near the surface. - Full-Field: Measurement techniques which can only reveal the stresses at a single point in the sample do not present the full picture. In some cases, these techniques can scan a sample to generate a stress map, but this is often exceedingly slow. Other techniques may be fast, but can only report global stress over the measurement sample. This means local regions of high stress, often the source of failure, cannot be resolved.

For comparison, a brief description of various competing stress measurement methods are presented below:

- Crossed Polarizers
- A set of crossed polarizers are, in essence, a plane polariscope. As described elsewhere, the plane polariscope operates on a similar principal to the techniques employed by Polaritek but is far more limited. The plane polariscope is typically a manual instrument which is operated by a human. The results are extremely subjective and generally qualitative at best. In some cases, estimates of maximum shear stress can be made by eye, but this becomes difficult when the fringe order is very low or high. Due to the isochromatic/isoclinic interaction, misleading results are often encountered. Read more here »

- Raman Spectroscopy
- Raman is a non-destructive technique which can observe the vibrational modes of a measurement sample by observing inelastic scattering from a laser. These vibrational modes can be related to atomic spacing and ultimately to stress. Measurements from Raman Spectroscopy are highly localized – often with a spot size of only 10 µm or less. Since information is gathered through surface scattering, only the stresses very near the surface of a sample can be determined. Then, depending upon wavelength, the depth of penetration may vary from a few hundred nanometers down to a few nanometers. Although measuring stress at a single point is very fast, generating a full-field stress map requires 10s or 100s of minutes to complete.

- X-Ray Diffraction
- In X-Ray Diffraction (XRD), atomic lattice spacing is determined through diffraction of X-Rays according to Bragg’s Law. Similar to Raman Spectroscopy methods, surface stress can only be measured at a single point on the surface of a sample. Although the spot size is on the order of millimeters and the depth of penetration is on the order of microns, the measurement time is similar to Raman Spectroscopy. It is also important to note the special precautions which must be taken to work with X-Rays.

- Surface Profile (Stoney Equation)
- One technique which can estimate the global stress in a thin film deposited on a measurement sample is to measure the deflection or bow of the sample both before and after deposition, then apply the Stoney Equation. To measure the deflection of a sample, often a stylus profilometer is utilized. This is a time consuming process which requires contact with the measurement sample. Laser based systems are faster and do not require contact, but the other limitations remain. Read more here »

^{[1]} Prevéy, P.S., Practical Applications of Residual Stress Technology, ed. C. Ruud, pp 47-54, Am. Soc. for Met., Materials Park, Ohio (1991).