WO2000012962A1

WO2000012962A1 - Method for strain deformation

Info

Publication number: WO2000012962A1
Application number: PCT/FI1999/000674
Authority: WO
Inventors: Markku Käppi
Original assignee: Kaeppi Markku
Priority date: 1998-08-28
Filing date: 1999-08-13
Publication date: 2000-03-09
Also published as: EP1108196A1; FI981844A0; FI104761B; AU5293099A

Abstract

The present invention is related to a method for determining strains as well as deformations related to the same on the surface of objects (1) such as metal containers and the like, in which method a brittle material known as a strain-indicating brittle coating, e.g., brittle lacquer is applied on the surface of the object while the object is still unstrained and, subsequently, the object is strained, advantageously at least up to the strain level corresponding to its operating conditions, whereby the strain-indicating coating develops cracks (4) as the strain exceeds the nominal cracking limit of the coating, thus indicating suitable locations for the placement of a strain gage or a plurality of different types of strain gages (A, B, C) such as rosette strain gages for a more precise stress measurement or determination of strains. According to the invention, on the basis of information gathered from the strain crack (4) of the brittle coating, the measurement value of at least one strain gage is extrapolated in desired directions to desired points representing, for instance, a high probability of fatigue failure.

Description

Method for strain deformation

The present invention relates to a method for determining strains as well as deformations related to the same on the surface of objects such as metal containers and the like, in which method a brittle material known as strain- indicating brittle coating, e.g., brittle lacquer is applied on the surface of the object while the object is still unstrained and, subsequently, the object is loaded up to a stress level advantageously not less than that of its operating condi- tions, whereby the strain-indicating coating develops cracks as the strain exceeds the nominal cracking limit of the coating, thus indicating suitable locations for the placement of a strain gage or a plurality of different types of strain gages such as rosette strain gages for a more precise measurement or determination of strain variations.

One major art of technology having great use of strain measurement is the transportation sector utilizing shell constructions, an exemplifying embodiment of which to be discussed later in the text is represented by the container of a tank truck, whose manufacture involves complicated engineering and a design prone to shape imperfections. A practicable approach to the design process which is complicated by such shape imperfections has been sought for a long time without reaching a good solution. Investigations into fatigue-resistant constructions and, particularly, the practical tests thereof in order to determine the required material thicknesses and structural details are costly and time- consuming. Testing of welded constructions such as containers is complicated by the difficulties met in a reliable placement of strain gages on suitable locations that on the welds is an almost impossible task. Also the correct orientation of the strain gage and, particularly, the optimum location thereof is difficult. Herein, great aid is found from use of a brittle lacquer.

According to conventional techniques of finding the points of maximum stress, brittle lacquer or other similar brittle coatings are employed in the following manner: firstly, the surface of the object is sprayed with thin lacquer layers having a thickness of about 0.05 mm. The lacquer is applied by spraying and then dried in open air. Additionally, a layer of reflective undercoat may be used under the brittle lacquer. As the object is then tested under a stress, the lacquer will crack when the local strain exceeds the cracking limit of the lacquer layer. Typically, the nominal cracking limit of brittle lacquer is 500 μm/m. Lacquer cracking occurs first at points of highest tensional strain, thereby indicating the concentration areas of stresses. Furthermore, the strain cracks indicate the direction of tensional stress by way of occurring at right angles to the main direction of the stress. In this manner, the critical areas are found on which the strain gages should be located for a maximally accurate test result.

Although brittle lacquer in principle offers accurate strain gage placement and orientation, the indicated location of a stress concentration is often extremely complex to measure by being subjected to a multiaxial stress in a real loading situation and, moreover, inasmuch the stress increases in a stepwise manner according to the behavior of the construction under a fatiguing load. In a welded structure, the greatest stresses (strains or tension) occur in a welding defect that generally is located in the immediate proximity of the weld at a point not permitting any gage to be placed thereon. In the most disadvantageous case, the direction of stresses is at a right angle to the weld.

When a metal surface, e.g., the surface of a container, is already under a stress, the placement of a strain gage is impossible at a critical point, e.g., that formed between the cradle and the container resting thereon. Then, the measurement must be made, e.g., from the inside of the container. This technique requires complex protective procedures, and the measurements must be carried out for correct loading results by way of using a water filling. Furthermore, as the measurements are made from the "wrong" side, the results are clearly less reliable. On the other hand, certain types of continuous strain cracks may sometimes be "seen" as a concentration of brittle coating cracks on the reverse side of the wall, at a point coinciding with the location of the fracture. Herein, one possible test method is to subject the container structure to a torsional load, for instance.

Due to discontinuities of the smooth surface of a structure, the strain gage cannot always be placed at a desired location. For instance, in welded container structures the strain gage must be placed over the smooth surface of the container wall, at a close proximity to a welded seam. Herein, the increase of stress due to a discontinuity of the weld and a possible wedge edge defect such as an undercut notch must be taken into account in some other manner. In practice, the measured value of strain/stress must be extrapolated in a reliable manner to the point of the worst-case load typically occurring at the location of said weld defect. This extrapolation can be performed to within a certain margin using the numerical methods of stress analysis. If the parameters of the weld seam geometry are known, the dimensioning of the structure may also be carried out utilizing fatigue estimation techniques published in the SAE standards.

Generally, the stress peak caused by a structural discontinuity in a container construction cannot be identified in a reliable and straightforward manner during the container design stage. In simple cases pertaining to containers having a shell sufficiently thick-walled to be free from shape imperfections, the design computations can be based on the finite-element method (FEM) which is rather tedious to apply due to the ill-defined structure of welded seams (necessitating the use of weld quality statistics), among other problems. The increase of stress close to a weld is often difficult to control. In thin-walled containers (implemented as shell structures), the secondary bending stresses caused by shape imperfections undermine reliable FE modelling. In fact, the stress situation is complicated in any container if or when a crossing weld occurs in an area. A typical example of this is the meeting point of the flat butt weld of the container shell envelope with the shell end nozzle welds. The situation will become ever more difficult if a bracket, a pipe feedthrough, change of material thickness or other similar discontinuity occurs at the same point. Practical experience proves that a fatigue failure will occur within the same area of discontinuity, often at the very same point. Complete dimensioning is impossible on the basis of a simplified theoretical model. In reality, the situations typically are very complicated, whereby the use of finite element methods becomes expensive, unreliable or even impossible depending on the degree of complexity in the construction. Then, experimental methods of dimensioning must be employed. Dimensioning may also be carried out with the help of a prototype or, alternatively, based on measurements made on test pieces.

If it seems necessary and profitable, a stress test can be performed in a relatively reliable manner using a plurality of strain gages glued over the same area. Herein, it is advantageous to make use of so-called rosette strain gages suited for multiaxial measurement. The strains in a smooth plate confined to within the area enclosed by the strain gages can be estimated very reliably with the help of a linear model, for instance. Shape imperfections of the container may complicate the situation. Excluding a possible defect in the edge zone of the weld, also the increase of stress due to the geometry of the weld seam can be estimated by the linear method using two or three strain gages placed at a suitable distance from each other. Conventionally, this technique is called the hot-spot stress measurement. To determine the hot-spot stress, the engineering literature of the art recognizes three methods: computation using the finite- element model, multiplication of the nominal stress by a possibly known stress concentration coefficient and experimental determination of stresses by means of strain gages.

In spite of its uncertainty factors, the multiple strain gage method may offer a sufficiently good accuracy for practical tests, but is clumsy and therefore expensive to implement. For comprehensive tests, the number of strain gages needed may be as many as hundred strips. During later analysis of the measurement results, there often arises a further need to know the stress value at some point close to the installed strain gages. In practice, this information generally is acquired so that a new gage is glued at the desired point, the conductors are attached to the strain gage and the required measurements are made. All these procedures require a lot of work, particularly if the original setup of measurement instrumentation has already been dismantled as usually is the case.

It is an object of the present invention to provide a method that is simpler to use than those of the prior art and yet offers a sufficiently high degree of reliability. The method according to the invention is characterized in that, on the basis of information gathered from the cracking of a brittle coating, the measurement value of at least one strain gage is extrapolated in at least one arbitrary direction to a desired point or points representing, for instance, a high probability of fatigue failure. Such a point is, e.g., the bottom of a weld undercut exhibiting the maximum value of local strain which generally is computed using the Neuber rule, for instance. The brittle lacquer coating used herein may have an extremely thin layer thickness, even smaller than 0.01 mm.

An embodiment of the invention is characterized in that the number of strain cracks of the brittle coating is counted from a rigid portion of the structure over a length equivalent to that to be measured, next an equivalent count is taken on another portion of the structure, e.g., on a thinner portion, whereby a higher number of strain cracks is encountered over the length being measured, and finally the corresponding strains or variations of strains are determined as being proportional to said numbers of said counted cracks.

Another embodiment of the invention is characterized in that a strain gage measurement is performed over said selected crack concentration, and the behavior of the construction such as the variation of stress measured using at least one strain gage is extrapolated by means of the cracking information obtained from said brittle coating in a linear ratio to a desired point and direction.

One of the basic concepts of the invention is that, within the linear portion of a stress-strain curve, the variations in the load or stress in principle are inversely proportional to the local thickness of the material.

By virtue of the invention, stress measurements can be performed in a manner that is simpler and more economical than any of the prior art. Furthermore, the reliability of measurement results is improved. One additional benefit of the invention is that stress extrapolation can be made starting from any strain gage in a multiple strain gage layout and particularly for shell constructions within certain limits, toward an arbitrary direction by properly taking into account the taper of the shell. This means that extrapolation in practice with due caution is possible starting from a strain gage (or even from a stress value which computed in a reliable manner) whose location may be substantially far removed from the point to be extrapolated. In principle, the method can be implemented using only one strain gage. The rosette-type strain gage has been found a very useful choice. As the strain cracks of the brittle coating indicate the direction of the main stress, an extra benefit can be obtained at both the strain gage and the hot spot: if the stresses for some reason are not uniaxial, a corrective computation can be performed. This is a situation often encountered, e.g., at the corners of shell constructions, particularly in conjunction with intermittent welds. One more advantage of the method is that due to stress calibration the cracking limit of the brittle coating used bears no major significance, which permits the use of inexpensive stress indicator coatings and other cost-effective brittle coatings such as chalk slurry or replacement of a professional-use brittle lacquer by cheaper hard lacquers (of a cracking nature).

In the following, the invention will be described in more detail with reference to the illustrated exemplifying embodiments.

A basic embodiment of the method according to the invention can be appreciat- ed by examining a technique in which first the number of strain cracks is recorded on such a length of a durable material that is equal to the length to be investigated (using a 2 mm thick plate, for instance). Next, the same measure- ment is also made on a thinner material. Hereby, a higher number of strain cracks will be found over the same distance of counted cracks. As the strains or variations of strains present in these two cases are proportional to the number of cracks recorded in both cases, the method already at this stage offers a simple technique of reliably making quick tests serving to assess the need for further investigations. Herein, a certain crack concentration (e.g., 6 cracks/cm) is set as the limit above which fatigue analysis at the test point is justified.

Fatigue analysis with the help of the brittle coating is carried out so that a strain gage measurement is performed at a selected concentration of counted strain cracks (e.g., applying a limit of 4 cracks/cm). The stress behavior of the construction measured by the strain gage (e.g., variation of stresses) is extrapolated with the help of the brittle coating information in a linear ratio to the desired point. For instance, if the crack density at the desired point of extra- polation is 8 cracks/cm, also the value of stress variation is multiplied by an extrapolation factor of two. If the lower limit for fatigue analysis is chosen to be the above-mentioned 6 cracks/cm, the analysis is worthwhile.

In the preliminary stage of the stress test, the brittle coating can be used as follows: if a point on the construction is suspect to excessive stress, a coating of suitable cracking or even peeling character can be sprayed thereon. From the crack density of the brittle coating under a load can be estimated the possible need for further studies. The crack density of the coating has been found to indicate stress variations along the surface of the plate in a sufficiently reliable manner for practical purposes. When no cracking can be seen on the applied brittle coating such as a chalk slurry or the like, the strains are below the cracking limit of the coating, meaning that either the point is not subject to a fatigue failure or an incompatible coating is being used. Areas subjected to multiaxial stresses are effectively detected by means of an easily peeling coating. For instance, hardened chalk slurry flakes off in this manner.

Subsequently, the indicated fatigue-critical location can be investigated by the more accurate brittle lacquer method. When necessary, the values of the notch shape factor and the notch fatigue resistance reduction factor can be determined according to their definitions: the notch shape factor is the ratio of the actual stress elevated due to the local discontinuity to the nominal stress in the material. This parameter may often be calculated directly from the number of strain cracks at the stress concentration point. Respectively, the notch fatigue resistance reduction factor is defined as the ratio of the ultimate fatigue strength of an unnotched object to that of a notched object. The determination of notch fatigue resistance reduction factor is performed by subjecting the discontinuity to a bending stress and then comparing in the same fashion the increase of crack density at the critical point to that of a "smooth" area of the object.

The brittle coating method according to the invention is also advantageously applicable to the determination of the hot-spot stress discussed above. From the crack density of the brittle coating, the measurement result of a strain gage can be extrapolated to the hot spot. In addition to the hot-spot stress, the method can be used for determining a stress concentration at a heat-affected zone of a weld, e.g., at the bottom of a root penetration defect. Next, the latter case is elucidated with reference to the attached drawings in which

Fig. 1 shows generally the principle of the measurement/extrapolation of hot- spot strains in a weld;

Fig. 2 shows a top view of the weld of Fig. 1 having three uniaxially measuring strain gages placed thereon after a brittle coating test; and

Fig. 3 shows basically the same layout as Fig. 2, but now under a different tensional stress.

Referring to Fig. 1 , therein is shown a cross-sectional view of, e.g., a wall 1 of a container with a plate 2 or similar element welded thereon. The weld is denoted by reference numeral 3. The stresses under load at different points of the container wall are denoted by arrows. To measure the stresses, three strain gages A, B and C are placed on the wall surface of the container.

In Figs. 2 and 3 are shown diagrammatical layouts illustrating the method of determining the hot-spot stresses by means of strain cracks 4 of the brittle coating. To this end, the point under study is covered with a brittle lacquer or similar coating, after which the object under study is subjected to a load advantageously simulating that of the actual operating situation. Then, the brittle coating develops cracks as soon as its limit of cracking is exceeded.

Next, the strain at the cracks can be extrapolated from the measurement values of strain gages A, B and C in any arbitrary direction and to any point thereabout by drawing on the information obtained from the strain cracks of the brittle coating. In the case shown in Fig. 2, the strain cracks 4 are parallel to the edge line of the weld, while in Fig. 3 the cracks on the plate are inclined to an angle of about 30° in regard to the edge line of the weld. Over the weld, the crack lines are further inclined by about 30°. This information cannot be obtained by means of, e.g., rosette strain gage measurements (without the aid of the cracking coating method), since the strain gage cannot be mounted on a weld. The discussed situation is typical and critical in conjunction with, e.g. a skip weld made to a plate structure. The arrows in the diagram indicate the directions of the major strains.

Also the above-discussed problem of tedious post-measurements in vicinity of the strain gages can be solved by means of the method according to the invention: when the stress situation at a point earlier measured by means of strain gages is known, with the help cracking information obtained from the brittle coating applied later on the same area, the stress values may be later extrapolated to a desired point such as the edge of a weld. If the major component of stress is at an inclined angle (e.g., 45°) to the weld edge, the exact angle at which the stress lines cross over the weld is generally difficult to assess by conventional means. For instance, if the stress lines cross the weld essentially parallel to the weld, the situation is far less critical than in a more angled crossing. In the worst case, the major component of stress may be entirely perpendicular to the weld. However, these details are difficult to resolve in a shell structure in a conventional manner. Herein, the brittle coating technique offers an easy and reliable approach to verify the stress situation after strain measurements.

The above-described method may be utilized for stress comparisons between individual specimens of a product, too, as well as for establishing a stress history of products or constructions already taken into use. The practical execution of the method is a simple task requiring only the spraying or other application of the brittle lacquer on the desired point, followed by a load test. The practical test can be carried out in field conditions, e.g., in a workshop. To ascertain and calibrate the method in workshop conditions, tests must be performed at areas already measured using strain gages. Also simple bending tests on pieces, sheet metal strips, weld test piece made therefrom and other objects are easy to make using the brittle coating. In spite of the relatively simple nature of the tests, the information submitted by them is extremely valuable.

Generally, the local strain variations at the tip of a notch (e.g., a weld root penetration defect) can be determined directly with the help of the brittle coating method. Hence, the strain situation at the notch tip need not be calculated in the traditional manner using the rather clumsy and inaccurate rules of Neuber and Glinka, whereby the local strain is typically determined from the Ramberg- Osgood stress-strain relationship.

The SAE-method-based fatigue design aims to achieve maximum accuracy in regard to the local stress concentration. The present invention offers a method of determine the local strain, e.g., at the tip of a notch running along the edge line of a weld, directly by means of cracks developing in a suitable brittle coating applied thereon. To those versed in the art, it is obvious that the invention is not limited to the exemplifying embodiments described above, but rather can be varied within the scope and spirit of the appended claims.

Claims

Claims:

1. Method for determining strains as well as deformations related to the same on the surface of objects (1) such as metal containers and the like, in which method a brittle material known as a strain-indicating brittle coating, e.g., brittle lacquer is applied on the surface of the object while the object is still unstrained and, subsequently, the object is strained, advantageously at least up to the strain level corresponding to its operating conditions, whereby the strain- indicating coating develops cracks (4) as the strain exceeds the nominal cracking limit of the coating, thus indicating suitable locations for the placement of a strain gage or a plurality of different types of strain gages (A, B, C) such as rosette strain gages for a more precise stress measurement or determination of strains, c h a r a c t e r i z e d in that, on the basis of information gathered from the strain cracks (4) of the brittle coating, the measurement value of at least one strain gage is extrapolated in desired directions to desired points representing, for instance, a high probability of fatigue failure.

2. Method according to claim 1 , c h a r a c t e r i z e d in that the number of the strain cracks of the brittle coating are counted from a rigid portion of the structure over a length equivalent to that to be measured, next the equivalent count is taken on another portion of the structure, e.g., on a thinner portion, whereby a higher number of strain cracks (4) is encountered than those counted over the length being measured, and finally the corresponding strains or variations of strains are determined as being proportional to said numbers of said counted strain cracks (4).

3. Method according to claim 1 , c h a r a c t e r i z e d in that a strain gage measurement is performed over said selected crack concentration, and the behavior of the construction such as the variation of stress measured using at least one strain gage (A, B, C) is extrapolated by means of the cracking information obtained from said brittle coating in a linear ratio to a desired point and direction.