Measuring residual stress - yesterday and today

Bryan Martin joined TWI in 1966 after four years as a prototype machine and tools project engineer, at Mansols GB. Before that he served a six year mechanical engineering apprenticeship as an R&D tool and instrument maker at Sheppard & Tulloch Tool & Instruments. Since joining TWI Bryan has been heavily involved in the strain measurement department, and furthered residual measurement on all types of welded components using the centre hole air-abrasive measurement system at TWI and in Europe.

Early in the 20th century very little was known or understood about residual stress. Most engineers knew it was there in some form or other and accommodated it. As Bryan Martin reports, it was another problem trying to measure residual stress.

In 1934 engineers decided to investigate the magnitude of residual stress, hence the need to develop a system to measure these stresses.

Not all residual stresses are a problem but they can increase the tendency towards brittle fracture, reduce stability under compressive loading, and cause some reduction in fatigue strength.

In some cases residual stresses can be an advantage and are deliberately introduced by engineers, using methods such as hammer peening, shot peening or spot heating, to improve fatigue life.

Residual stress measurement methods may be split into three categories:

• Fully-destructive such as block removal, slicing, splitting or layering
• Non-destructive, such as X-ray diffraction, neutron diffraction, ultrasonic or magneto-elastic and high precision extensometer methods
• Semi-destructive such as abrasive jet centre hole or trepanning

Residual stresses are often difficult to determine with purely analytical or numerical methods because of the many materials used in engineering today, and the complexity of welded structures and components. Hence the need exists to have equipment to measure residual stress in these components.

The centre hole abrasive jet method

Mathar ^[1] in 1934 used a 2-step drill method using very early strain gauges, At this time the centre hole gauge was not available. Rendler and Vigness ^[2] in 1966 used a specially dressed end-mill using some early centre hole gauges. It was not until 1973 when Bush and Kromer ^[3] investigated various methods and came up with abrasive jet machining.

In 1976 Beaney and Procter ^[4] investigated the method still further and used an orbiting head system which we use today known as the abrasive jet machining method.

This article describes the technique, ^[5] the equipment, and two special purpose pieces of equipment known as the Tubestress and Cornerstress units, designed and built by TWI. These have been used for the past 25 years in the laboratory and in the field, for TWI members with great success.

CEGB Procter and Beaney Abrasive Jet System

In the latter part of the 20th century it became most desirable, if not essential, to be able to carry out measurements on operational welded structures and components of all shapes and size.

Criteria required of the technique are: ^[6]

• It must be non-damaging in terms of size and thickness of components to be tested.
• It must measure bulk surface stresses (macrostresses), ie those that would influence the initiation and propagation of cracks.
• The equipment must be portable, it must be possible to use in confined spaces.
• To minimise shutdown times it should be quick and easy to use.

After a great deal of detailed investigation, it was considered that the centre hole technique could satisfy all the requirements, as long as an acceptable accuracy of the hole size, and positioning of the drilled hole could be attained and maintained to standard. ^[7] A nominal hole size of 1.6mm diameter, 1.6mm deep could be accepted as non-destructive on large size and thick components.

Investigation of the centre hole technique looked at all the factors that could influence the measurement accuracy, including the effects of machining the hole and the practical and physical problems with its application.

The results of these investigations were a hardware package produced by Beaney and Procter of the CEGB. The system involved machining a larger hole of a nominal 2mm diameter, 1.70mm deep, by stress-free abrasive jet machining using a rotating jet and aluminum oxide 53 micron grit through the centre of a special three element rosette strain gauge.

Measurements are relatively quick and easy to carry out. Between three and seven a day can be made on a flat surface by a skilled technician. The hardware package can be used in all planes provided the appropriate fixture and fittings are made.

The abrasive jet technique can machine all types of materials including high carbon steels, hardened steels, stainless steel, copper, aluminium, titanium alloys and many others and has done so at TWI.

Principle of the centre hole technique

The principle of the technique is shown in Fig.1, where the residual stress is indicated by σ _R.

When the hole is drilled the stress must reduce to zero at the edge of the hole, the stress field is modified in the manner shown. The centre hole strain gauge indicates a change in strain related to the corresponding stress change shown by the shaded area.

In general analytical work stress fields will be biaxial and the directions of principal stress will be unknown. So a three element rosette strain gauge is needed. For any given value of σ _R the strain changes detected by the strain gauge will vary with the distance 'x'. It is imperative that the drilled hole is the same known distance from each of the three elements of the strain gauge rosette, ie it must be perfectly round, and in the centre of the strain gauge rosette and of a known diameter for good accuracy.

Calculation of residual stresses assuming elastic behaviour

The residual stresses are derived from the measured strains using the formulae given by Beaney and Proctor. ^[4]

where:

σ _min , σ _max are the minimum and maximum principal stresses in N/mm ² .

are the strain changes in microstrain at the three gauge elements, caused by machining the hole.
E is the elastic modulus in MN/mm ² .

l/K _l is a calibration constant which is dependent on the ratio of hole diameter to the pitch circle diameter of the gauge elements. Values of l/K _l for the standard design of centre hole gauge with a mean gauge radius of 2.57mm were tabulated by Beaney ^[8] as a function of hole diameter, and may also be expressed by the following polynomial function:

l/K _l = 32.5696 - 35.6232d + 14.6067d ² - 2.1177d ³

d is the hole diameter.

vK ₂ /K _l is taken to be equal to 0.3.
The direction, θ, of the maximum principal stress, measured clockwise from gauge element 1, is derived from:

If ∈1 ≤ ∈3, θ = α

If ∈1 > ∈3, θ = α + 90°

The stresses in a Gauge element 1 and Gauge element 3 directions are given by:

Accuracy of the method

Hole alignment is better than 0.013mm. Any errors will depend on the direction of misalignment with respect to the stress field and rosette direction. At worst, it will be similar to the effects of the hole diameter which is ±1.2%. It has been concluded that abrasive jet machining stresses are negligible.

A detailed investigation of the accuracy of this method has been carried out by Beaney. ^[8] The standard abrasive jet equipment forms a parallel sided hole shown in Fig.2 as the jet nozzle rotates it will leave a central spigot. This does not affect the measured strain relief.

Typical operating parameters for abrasive jet machining of a 2mm diameter 2mm deep hole are shown in Fig.3 in high carbon steel.

Fig.3. Operating parameters

The formulae due to Beaney and Proctor ^[4] which are used to derive the residual stresses from the measured strains and hole dimensions are a modified version of the standard formulae for the interpretation of a conventional three-element rectangular rosette gauge, in which all strains are scaled by the parameter -1/K ₁ and Poisson's ratio is replaced by the term vK ₂ /K ₁ . Errors in -1/K ₁ correspond to errors in the measurement of hole diameter, which have been discussed above. Beaney and Proctor ^[4] determined empirical values of νK ₂ /K ₁ from twelve calibration tests performed by various workers between 1956 and 1974. They found values in the range 0.3 ± 12%, and showed that this could give errors of up to ±5.2% in the derived stresses.

Beaney ^[8] investigated the effect of plasticity at the edge of the hole on the apparent stresses measured by the centre hole method assuming fully elastic behaviour. Beaney's experimental data showed that the errors due to plasticity effects are less than 2% for uniaxial or equibiaxial stresses up to 75% of yield, or for shear stresses up to 65% of yield.

Hence, the total measurement error using the standard CEGB abrasive jet equipment is 10.2%, including the effects of strain measurement, diameter measurement, hole misalignment, analysis method and hole edge plasticity for stresses up to 65% of yield.

Equipment

The standard equipment ( Fig.4) comprises a powder control unit, drilling head, and optical microscope for measuring diameter and depth, also aligning the cutting head over the strain gauge, compressor and a grit extractor, ie vacuum cleaner and a strain measuring instrument with a least three channels. Typical residual stress strain gauges are shown in Fig.5 and 6.

Tubestress and cornerstress equipment

Tubestress

The standard centre hole equipment has access limitations, because it requires at least 400mm head room and 30mm clearance from internal corners, so to make measurements in tubes with inside diameters of less than 400mm it is impossible to use. Hence the need for a piece of equipment that would carry out these measurements.

TWI developed this piece of equipment which will measure residual stresses inside 70mm tubes and to a depth of 300mm.

The equipment was designed and developed to operate in the vertical position with 360° rotation. It operates equally well in the horizontal plane, provided the appropriate fittings and fixtures are made.

The Tubestress unit has a fibre optic borescope with cross hair wires for viewing and aligning the centre hole gauge. A fixed carbide nozzle is mounted 20mm forward of the viewing lens. An air and powder mix of 53 micron abrasive grit is used through the nozzle to machine the hole typically 2mm deep and 2mm diameter.

Figure 7 shows a typical abrasive jet machined hole using a fixed carbide nozzle as used on the Tubestress and Cornerstress equipment.

The fibre optic borescope support tube and nozzle are mounted on three-axis micrometer slides ( Figs 8-10). These allow very accurate positioning over the strain gauge target. Once aligned, the nozzle is then located over the strain gauge at a predetermined offset. After machining, the micrometers slides are used to measure the diameter and position of the centre hole. The alignment accuracy of the machined hole with the centre of the gauge is critical: the tolerance on the hole eccentricity is 20 microns.

Cornerstress

Cornerstress equipment is for residual stress measurement locations 11mm from internal corners, it uses identical three axis slides, a shorter fibre optic borescope and the same type of carbide nozzle jet ( Figs 11 and 12). The principles are the same as the Tubestress unit and identical alignment procedures, ideal for measuring close to fillet weld toes with large vertical plates attached.

Both pieces of equipment have been used on large projects at TWI and in Europe.

Accuracy

There are various possible sources of error associated with the measurement of residual stresses using the TWI Tubestress and Cornerstress equipment. They are as follows.

Hole diameter and eccentricity

The error in residual stresses due to an error in hole diameter can be determined by the change in the calibration constant 1/K ₁ . A measurement error of the diameter ± 0.020mm for a hole diameter of 2.000mm gives a change in calibration constant of ±1.9%.

Errors in residual stresses due to the hole being offset from the centre hole target can be determined from Ajovalasit's formula. ^[9] For an offset of ±0.020mm, the maximum error in the calculated stresses in the x and y direction is ±1.6%.

Hole depth

Beaney ^[8] has shown that for holes of about 2mm diameter the relaxed strain is insensitive to depth, provided the depth is greater than 1.6mm. As long as this depth is maintained, it is assumed that there are no errors due to hole depth.

Hole profile and roundness

The nozzle used in the Tubestress and the Cornerstress units are a fixed carbide type, this was pioneered by Fidler. ^[10] He demonstrated with improved geometry that this type of nozzle produced holes with parallel sides. He never encountered any problems with hole out of roundness after machining many hundreds of holes. Hence it is assumed there are no errors due to hole out-of-roundness.

Strain measurement, analysis method and hole edge plasticity

The estimated errors due to these factors are the same as for the CEGB equipment, namely ±0.6% for strain measurement, ±5.2% for analysis method, and ±2% for hole edge plasticity for stresses up to 65% of yield.

Total errors

Hence the total estimated error for measurements made using the Tubestress or Cornerstress equipment is ±11.3%, compared with 10.2% for the CEGB equipment.

Summary

TWI has carried out many hundreds of residual stress measurements both at TWI and abroad, using the standard CEGB centre hole system, and TWI Tubestress and Cornerstress equipment on all types of components and structures.

The centre hole abrasive jet method is a valuable tool for the measurement of residual stress.

References