Water turbine curved surface part residual stress testing system based on ultrasonic method

Abstract

The invention discloses a water turbine curved surface part residual stress test system based on an ultrasonic method, which relates to the technical field of residual stress detection and comprises a blade surface modeling module, an ultrasonic sound time acquisition module, a co-site sound time comparison module, an anomaly judgment module and a residual stress distribution heat map generation module. According to the method, co-location measurement points of multiple blades are determined by constructing a unified coordinate system, the difference of ultrasonic propagation time between the co-location points is collected and calculated to obtain the relative difference of residual stress, a preset threshold value is used for marking the residual stress abnormal position, and a heat map is generated for display. According to the method, the problems that the stress concentration area in the large curved-surface blade group is difficult to identify and the stress distribution difference is difficult to evaluate quickly under the condition of lack of unstressed reference are solved by utilizing the periodical characteristics of geometry and materials of multiple blades of the water turbine.

Description

Technical Field

[0001] This invention relates to the field of residual stress detection technology, and more specifically, to a residual stress testing system for curved surfaces of water turbines based on ultrasonic methods. Background Technology

[0002] As the core equipment of a hydropower station, the turbine blades inevitably accumulate residual stress during manufacturing and long-term operation. The presence of these residual stresses is often a significant contributing factor to fatigue cracking and even fracture failure in the blades. Therefore, effective detection and monitoring of residual stress in turbine blades, especially in their complex curved surfaces, is crucial for ensuring the safe operation of the unit. Among existing non-destructive testing techniques, ultrasonic testing is widely used due to its strong penetrating power and sensitivity to internal stress. Its basic principle is based on the acoustoelastic effect, where the propagation speed of ultrasonic waves in a material changes slightly with variations in the internal stress state.

[0003] However, when using ultrasonic methods to measure absolute residual stress, a thorny problem is often encountered: the ultrasonic propagation time of the tested material in a stress-free state, i.e., the zero-stress reference, must be known. Traditional methods often require the fabrication of a zero-stress calibration block made of the exact same material as the workpiece being tested, which is a rather cumbersome process, especially when dealing with multiple curved blades.

[0004] It is worth noting that turbine runners typically consist of multiple blades with identical geometric designs, exhibiting significant structural periodicity. These blades are manufactured using the same mold or CNC program, resulting in highly consistent geometric dimensions and, due to the use of the same materials, acoustoelastic coefficients tend to be uniform. However, due to uneven casting cooling, differences in welding heat input, or varying operating conditions, the residual stress distribution at the same location on different blades may differ. If this geometric and material periodicity can be effectively utilized, it may be possible to test the relative relationships of residual stresses among different turbine runner blades in advance without the need for zero-stress calibration specimens. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a residual stress testing system for curved surfaces of water turbines based on ultrasonic methods, so as to solve the problems mentioned in the background art. To achieve the above objectives, the present invention adopts the following technical solution: A residual stress testing system for curved surfaces of a water turbine based on ultrasonic methods includes: The blade surface modeling module is used to construct a unified surface coordinate system for multiple blade surfaces of the same turbine, select the same measurement points on each blade surface, and form a set of measurement points with the same parameter coordinates on different blades. An ultrasonic time acquisition module is used to acquire the ultrasonic wave propagation time at all measurement points; wherein, the ultrasonic wave emission position, emission angle, and receiving position of all measurement points within the same point set are identical. The same-site acoustic time comparison module is used to calculate the difference in ultrasonic wave propagation time between different measurement points within each same-site set, thereby obtaining the corresponding difference in residual stress. The anomaly detection module is used to mark measurement points where the residual stress difference within any set of locations is greater than a preset threshold as locations of residual stress anomalies. The residual stress distribution heat map generation module is used to mark the locations of residual stress anomalies or the differences in residual stress at each measurement point on each blade, and generate a residual stress distribution heat map to show the relative distribution of residual stress.

[0006] Preferably, the co-location acoustic time comparison module uses the following formula to obtain the relative difference in residual stress: ; in, Indicates the first The first leaf in the The relative difference in residual stress at each measurement point The acoustoelastic coefficient of the turbine blade material. For the first The first leaf in the Measured ultrasonic wave propagation time at each measurement point For the first The arithmetic mean of the ultrasonic wave propagation time of all leaves within a set of identifiable sites; The difference in the relative difference in residual stress between different points within the same set of sites is used to characterize the difference in residual stress between different points.

[0007] Preferably, the process by which the anomaly determination module obtains the location of the residual stress anomaly includes: Calculate the standard deviation of the relative differences in residual stress among all measurement points within the same set of locations; Construct a dynamic deviation threshold. Set as: ; in The standard deviation is... The coefficients are the preset confidence interval coefficients; If the absolute value of the relative difference in residual stress at a certain measurement point within the same site set is greater than If so, the corresponding measurement point will be identified as the location of residual stress anomaly.

[0008] Preferably, the confidence interval coefficient ranges from 2 to 3.

[0009] Preferably, the system further includes an absolute stress calibration module, which is used to select one blade from all blades as a reference blade, fabricate a zero-stress calibration blade based on the reference blade, and obtain the absolute residual stress value of each measurement point on the reference blade through the calibration blade. Based on the absolute residual stress value of the reference blade, and combined with the difference in residual stress of other blades relative to the reference blade calculated by the same-point acoustic time comparison module, the absolute residual stress values ​​of each measurement point on other blades are deduced.

[0010] Preferably, the absolute stress calibration module adopts the following strategy when selecting a reference blade: Count the number of locations marked as residual stress anomalies on each blade; The blade with the fewest residual stress anomaly locations is selected as the reference blade.

[0011] Preferably, the system is further configured with a typical mode construction unit; the typical mode construction unit is used to calculate the mean of the absolute residual stress values ​​at the same measurement points of all blades; and the distribution of the mean of the absolute residual stress values ​​on the blades is set as the typical residual stress mode of the corresponding turbine blades.

[0012] Preferably, the system further includes an absolute stress theory calibration module; the absolute stress theory calibration module is used for: Based on the standard three-dimensional geometric model of the blade, the theoretical propagation path of ultrasonic waves at each measurement point is measured. Select points on the blade that are pre-determined to be in a state of zero residual stress as zero-stress anchor points; Calculate the ratio field between the theoretical ultrasonic propagation path at all measurement points on the blade and the theoretical ultrasonic propagation path at the zero-stress anchor point; Multiplying the proportional field by the measured ultrasonic propagation time at the zero-stress anchor point yields the theoretical ultrasonic propagation time at each measurement point on the blade under zero residual stress. ; Based on the measured ultrasonic propagation time at the measurement point and the corresponding theoretical ultrasonic wave propagation time Calculate the theoretical stress distribution at the measurement points. : ; in, Indicates the first The first leaf in the The residual stress value at each measurement point The acoustoelastic coefficient of the turbine blade material. For the first The first leaf in the Measured ultrasonic wave propagation time at each measurement point.

[0013] Preferably, the location of the zero-stress anchor point is determined based on the following: calculating the variance or standard deviation of the ultrasonic wave propagation time of each measurement point within the set of corresponding points; and selecting one or more measurement points with the smallest variance or standard deviation as candidate zero-stress anchor points.

[0014] Preferably, the zero residual stress is verified by creating a corresponding zero residual stress calibration block at the candidate zero stress anchor point.

[0015] The advantages of this invention over existing technologies lie in its innovative utilization of the geometric and material isomorphism and potential stress differences among multiple turbine blades, solving the problem of difficulty in assessing stress distribution in the absence of stress-free calibration blocks. By establishing a unified surface coordinate system for multiple blades, this invention defines points at the same location on different blades as a set of co-location points and directly compares the differences in ultrasonic propagation time between these co-location points. Since the geometric path length and material of co-location points are nearly identical, the difference in propagation time directly reflects the relative fluctuation of residual stress. This method allows inspectors to quickly screen out abnormal areas where stress levels significantly deviate from the group without prior acquisition of an absolute zero stress benchmark, and to intuitively identify potentially dangerous blades through the generated residual stress distribution heatmap, greatly improving inspection efficiency and targeting. Furthermore, this invention introduces a dynamic deviation threshold judgment mechanism, automatically adjusting the judgment criteria based on the statistical standard deviation of co-location point data, which can effectively identify true stress concentration points while avoiding misjudgments caused by random errors in the measurement system. Based on this, the present invention also provides a solution for obtaining absolute stress: either the optimal blade with the most uniform stress distribution can be statistically selected for individual calibration, thereby calculating the absolute stress of all blades at low cost; or, without calibrating the blades, a theoretical stress-free acoustic time field can be constructed based on a geometric model and a sound path ratio field to further obtain an evaluation value of the absolute stress. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the turbine blades of the present invention; Figure 2 This is a schematic diagram of the present invention, which sets a set of corresponding sites on the blade; Figure 3 This is the overall flowchart of the present invention; Figure 4 This is a flowchart of the present invention based on the addition of absolute stress testing. Detailed Implementation

[0017] The specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0018] like Figure 1 As shown, a water turbine runner typically contains multiple blades with highly uniform geometry. These blades are often cast from the same mold or machined using the same CNC program, thus exhibiting significant periodic structural characteristics. For example... Figure 3 and Figure 4 The diagram shown is the overall flowchart of the present invention. The present invention utilizes this feature and combines the ultrasonic acoustoelastic principle to achieve rapid assessment and quantitative analysis of the residual stress distribution of the blade group without the need for destructive calibration of each blade.

[0019] The system of this invention mainly consists of a hardware acquisition section and a data processing software section. The hardware section includes a 3D scanner for acquiring the geometric shape of the blade, a high-precision ultrasonic transceiver card, and a multi-axis robotic arm or special tooling fixture equipped with an ultrasonic probe. The data processing software section runs on an industrial computer or high-performance server and integrates multiple functional modules, including a blade surface modeling module, an ultrasonic time acquisition module, a time comparison module for the same location, an anomaly detection module, and a residual stress distribution heat map generation module.

[0020] First, the blade surface modeling module is responsible for establishing a unified measurement benchmark. Since turbine blades are complex free-form surfaces, directly marking identical measurement points on the physical entity is extremely difficult. This module first imports the theoretical 3D design model of the turbine or a high-precision point cloud model obtained through a 3D scanner. The system establishes a unified surface coordinate system, typically with the central axis of the runner as the Z-axis and the characteristic edge of a particular blade as the reference starting surface. Under this coordinate system, the module parametrically maps the surface of each blade, for example, using UV unwrapping technology to map the surface to a 2D parameter domain. Based on this, the system plans a grid of measurement points covering key stress areas on the parameter domain of the first blade, and then, using rotational periodicity, projects the coordinate parameters of these measurement points to the corresponding positions on all other blades.

[0021] like Figure 2 As shown, this invention defines a set of measurement points with the same coordinate parameters on different blades as a set of congruent points. For example, if a turbine has N blades, and each blade has M planned measurement points, then the system will generate M sets of congruent points, each set containing N specific physical measurement point locations. This construction of congruent points ensures that subsequent comparative analysis is performed in strictly consistent geometric positions, minimizing sound path errors caused by positional deviations.

[0022] The ultrasonic time acquisition module is responsible for driving the ultrasonic hardware to acquire data. To ensure measurement accuracy, this module typically controls a robotic arm to precisely move the ultrasonic probe to each measurement point. During acquisition, the module strictly controls the probe's orientation, ensuring that the probe's central axis always aligns with the surface normal at the measurement point, and that the ultrasonic incident angle and the transceiver spacing of the dual-crystal probes remain consistent at all points of contact. The ultrasonic probe can simultaneously receive reflected ultrasonic waves; in some embodiments, an additional probe can be placed on the opposite side to receive transmitted ultrasonic waves. Regardless of which side it is placed on, the propagation time of the ultrasonic waves within the material can be recorded.

[0023] Furthermore, after acquiring the acoustic time data from all measuring points, the acoustic time comparison module at the same location begins operation. The core logic of this module lies in utilizing the statistical regularities of the group to eliminate unknown factors. In the absence of a zero-stress test block, this invention cannot directly determine the absolute acoustic time reference for a specific point. However, since all blades are theoretically geometrically identical, the thickness at the same location should be consistent. Therefore, this module calculates the statistical characteristics of the data within each set of locations at the same location. The system uses a specific formula to calculate the relative difference in residual stress: ; in, Indicates the first The first leaf in the The relative difference in residual stress at each measurement point The acoustoelastic coefficient of the turbine blade material. For the first The first leaf in the Measured ultrasonic wave propagation time at each measurement point For the first The arithmetic mean of the ultrasonic wave propagation time of all leaves within a set of common sites.

[0024] The above formula is adopted based on the following mathematical principle: According to the theory of acoustoelasticity, the blade and leaves Absolute residual stress at a certain point (i.e., at the same measurement point). and They are respectively: ; in This represents the ultrasonic wave propagation time at the same stress point. Since the two locations are the same, the corresponding... same; For the leaf The actual ultrasonic wave propagation time measured at the corresponding location; For the leaves The actual ultrasonic wave propagation time measured at the corresponding location; The actual stress difference between the two blades at the same location for: ; The stress difference between the two blades is calculated using the formula for the relative difference in residual stress of this invention. for: ;in j For the parameters of this same site; contrast and as follows: ; set up ;but: ; However, in ultrasonic stress testing of metallic materials, the acoustoelastic effect is a weak physical effect. relatively It is a very small value; in fact, it is the relative rate of change of ultrasonic wave propagation time caused by residual stress. Usually in to order of magnitude, therefore It approaches 1. That is to say, the residual stress difference between two blades at the same location calculated based on the relative difference in residual stress in this invention is almost the same as the actual residual stress difference obtained based on the actual stress-free reference condition.

[0025] The difference calculated by this invention This actually characterizes the degree of stress deviation of that point on the blade relative to the group average. If A positive and large value indicates that there is tensile stress above the average level at that location; conversely, a small value indicates compressive stress.

[0026] In a further embodiment, the anomaly detection module screens the calculated differences. This module first calculates the standard deviation S of the relative differences in residual stress across all measurement points within the same location set. The standard deviation reflects the degree of stress dispersion at that location across different blades. Subsequently, the module constructs a dynamic deviation threshold T, which is set to n times the standard deviation S. Here, n serves as the confidence interval coefficient, typically ranging from 2 to 3. When n is 2, the threshold covers approximately 95% of the normal fluctuation range; when n is 3, it covers approximately 99.7% of the normal fluctuation range. If the absolute value of the relative difference in residual stress at a measurement point exceeds this dynamic threshold T, the system determines that point as an abnormal residual stress location. The dynamic threshold is not a fixed value but automatically adjusts according to the stress dispersion at different locations. For areas where stress fluctuations are inherently severe (such as the weld heat-affected zone), the threshold automatically increases to avoid false alarms; for areas where stress should be gradual, the threshold automatically decreases to improve sensitivity.

[0027] The residual stress distribution heatmap generation module visualizes the above analysis results. In some embodiments, different colors can be used to map the relative differences in residual stress on the 3D model of the blade. For example, red represents high tensile stress deviation, blue represents high pressure stress deviation, and green represents near-average levels. For locations marked as abnormal, the system will highlight them on the heatmap or add special symbols to help inspectors identify potentially problematic stray blades at a glance.

[0028] To further obtain physically meaningful absolute residual stress values, this invention systematically designs an absolute stress calibration module. This module provides a technical path based on physical calibration. First, the system needs to select one blade from all blades as a reference blade. The selection strategy is based on the most robust principle, that is, counting the total number of locations marked as abnormal by the anomaly detection module on each blade, the blade with the fewest such locations is considered to have the best overall process quality control and the internal residual stress distribution closest to the design expectation, and is therefore selected as the reference blade. After selection, the reference blade is physically calibrated to create a zero-stress calibration blade, thereby measuring the absolute residual stress values ​​at each point on the reference blade. The calibration blade is usually obtained by stress-relieving heat treatment of the corresponding material blank followed by contour machining. Its geometry is consistent with the actual blade, and the internal residual stress is reduced to near zero through heat treatment and lightweight machining control, thus it can be used to obtain the ultrasonic propagation time under zero residual stress as a calibration value.

[0029] Ultrasonic propagation time under stress-free conditions, measured based on zero-stress calibrated blades. Combined with the measured ultrasonic propagation time at the measurement point Calculate the stress distribution at the measurement points : ; in, Indicates the first The first leaf in the The residual stress value at each measurement point The acoustoelastic coefficient of the turbine blade material. For the first The first leaf in the Measured ultrasonic wave propagation time at each measurement point.

[0030] Once this set of absolute values ​​is obtained, it can be combined with the difference between the other blades and the reference blade calculated by the same-point acoustic time comparison module. This allows us to obtain the residual stress of other blades; specifically, For the corresponding reference blade B At the same site j The relative difference in residual stress at the location. For any other leaf A At the same site j The relative difference in residual stress at the location, based on Add the actual B exist j Stress at the point You can get A exist j The residual stress at the point. This method greatly reduces costs, as only one calibration blade needs to be manufactured to achieve quantitative testing of all blades in the unit.

[0031] Furthermore, this invention also includes a typical mode construction unit. After accumulating absolute residual stress data for all blades, this unit calculates the average absolute residual stress at measurement points at the same location and defines this average field as the typical residual stress mode of the turbine blades of this type. This mode represents the inherent stress fingerprint under this manufacturing process and can be used to guide subsequent process improvements or as a benchmark library for future units of the same type.

[0032] In addition to the aforementioned methods that require physical calibration of the blades, this invention also provides another absolute stress theoretical calibration module that can calculate absolute stress without manufacturing calibration blades. The module's working principle is based on the geometric-acoustic time ratio.

[0033] First, the module calls the standard three-dimensional geometric model of the blade and uses a ray tracing algorithm to measure the theoretical path of each measurement point along the ultrasonic wave propagation path, i.e., the theoretical thickness. Next, the system needs to find an anchor point on the blade, a point pre-identified as being in a state of zero residual stress or low stress.

[0034] To scientifically determine this zero-stress anchor point, the system employs a statistical screening method. Specifically, the system calculates the variance or standard deviation of the ultrasonic wave propagation time at each measurement point within each set of locations. Physical principles indicate that residual stress is typically a random variable causing acoustic time fluctuations at the same location, while geometry and material microstructure are relatively stable. Therefore, the point with the smallest variance or standard deviation signifies that the acoustic time at that location is highly consistent across all blades, minimally affected by random residual stress, and is highly likely to be a region where stress is fully released or in a natural equilibrium state (such as the straight section at the blade root). The system selects these points with the smallest variance as candidate zero-stress anchor points, and, if necessary, fabricates small zero-residual-stress calibration blocks only at these candidate point locations for secondary verification, minimizing costs.

[0035] After determining the zero-stress anchor point, the module calculates the ratio of the theoretical ultrasonic propagation path at all measurement points on the blade to the theoretical path at the zero-stress anchor point, forming a proportional field. Assuming the blade material is homogeneous and the sound velocity is constant everywhere under stress-free conditions, the propagation time at each point should be strictly proportional to its propagation path. Therefore, multiplying the above proportional field by the measured ultrasonic propagation time at the zero-stress anchor point allows for the derivation of the theoretical ultrasonic propagation time at each measurement point on the blade under ideal zero residual stress conditions, denoted as […]. .

[0036] Finally, based on the measured acoustic time at each measurement point And the calculated theoretical stress-free sound time The system uses the acoustoelastic formula to calculate the theoretical stress distribution at the measurement point. The formula is: ; in, Indicates the first The first leaf in the The residual stress value at each measurement point The acoustoelastic coefficient of the turbine blade material. For the first The first leaf in the Measured ultrasonic wave propagation time at each measurement point.

[0037] Using this method, the present invention successfully constructs a virtual zero-stress blade as a comparison benchmark, thereby enabling the estimation of the absolute value of the total residual stress of each blade. This scheme ingeniously combines statistical screening, geometric inversion, and acoustoelastic theory, solving the industry problem of the lack of stress-free benchmarks for large curved surface components.

[0038] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A system for testing residual stress of a curved surface part of a hydraulic turbine based on an ultrasonic method, characterized by, The system comprises: a blade surface modeling module, configured to construct a unified surface coordinate system for a plurality of blade surfaces of the same hydraulic turbine, select the same measuring points on each blade surface, and form a homologous point set by the measuring points with the same parameter coordinates on different blades; an ultrasonic time acquisition module, configured to acquire ultrasonic propagation times at all the measuring points; wherein the ultrasonic emission positions, emission angles and receiving positions of all the measuring points in the homologous point set are the same; a homologous point time comparison module, configured to calculate the differences in ultrasonic propagation times between different measuring points in each homologous point set, so as to obtain the corresponding differences in residual stress; an abnormality determination module, configured to mark the measuring points with the differences in residual stress greater than a preset threshold in any homologous point set as residual stress abnormal positions; a residual stress distribution heat map generation module, configured to mark the residual stress abnormal positions or the differences in residual stress of the measuring points on each blade, and generate a residual stress distribution heat map for displaying the relative distribution of residual stress.

2. The system of claim 1, wherein, The homologous point time comparison module obtains the relative difference amount of residual stress by using the following formula: ； wherein, represents the residual stress relative difference amount of the th blade at the th measurement point, is the acoustic-elastic coefficient of the water turbine blade material, is the measured ultrasonic propagation time of the th blade at the th measurement point, is the arithmetic mean of the ultrasonic propagation times of all blades within the th same-site set; The difference between the relative difference amounts of residual stress of different points in the same homologous point set is used to represent the difference in residual stress between the different points.

3. The system of claim 2, wherein, The process of obtaining the residual stress abnormal positions by the abnormality determination module comprises: calculating the standard deviation of the relative difference amounts of residual stress corresponding to all the measuring points in the same homologous point set; constructing a dynamic deviation threshold, the dynamic deviation threshold is set to: ； wherein is the standard deviation, is a preset confidence interval coefficient; If the absolute value of the relative difference amount of the residual stress of a certain measuring point in the same site set is greater than , the corresponding measuring point is determined as the residual stress abnormal position.

4. The system of claim 3, wherein, The value range of the confidence interval coefficient is 2-3.

5. The system of claim 1 or 2, wherein, The system further comprises an absolute stress calibration module, which is configured to select one blade as a reference blade from all the blades, manufacture a calibration blade with zero stress based on the reference blade, and obtain absolute residual stress values of the measuring points on the reference blade through the calibration blade; Based on the absolute residual stress values of the reference blade, in combination with the differences in residual stress of other blades relative to the reference blade calculated by the homologous point time comparison module, the absolute residual stress values of the measuring points on other blades are calculated.

6. The system of claim 5, wherein, When selecting the reference blade, the absolute stress calibration module adopts the following strategy: counting the number of residual stress abnormal positions on each blade; selecting the blade with the least number of residual stress abnormal positions as the reference blade.

7. The system of claim 5, wherein, The system is further configured with a typical modal construction unit; the typical modal construction unit is configured to calculate the mean value of the absolute residual stress values of the measuring points at the same positions of all the blades, and set the distribution of the mean value of the absolute residual stress values on the blades as the typical residual stress mode of the blades of the corresponding hydraulic turbine.

8. The system of claim 2, wherein, The system further comprises an absolute stress theoretical calibration module; the absolute stress theoretical calibration module is configured to: measure the theoretical ultrasonic propagation distance of each measuring point based on the standard three-dimensional geometric model of the blade; select a point position on the blade confirmed as a zero residual stress state as a zero stress anchor point; calculate the proportional field of the theoretical ultrasonic propagation distance of all the measuring points on the blade and the theoretical ultrasonic propagation distance of the zero stress anchor point; multiplying the proportion field by the measured ultrasonic propagation time of the zero stress anchor point to obtain the theoretical ultrasonic propagation time of each measurement point on the blade in the zero residual stress state ; based on a measured ultrasonic propagation time at a measurement point and a corresponding theoretical ultrasonic propagation time a theoretical stress distribution of the measurement point is calculated : ； wherein, represents the residual stress value of the th blade at the th measurement point, is the acoustic-elastic coefficient of the material of the turbine blade, represents the measured ultrasonic propagation time of the th blade at the th measurement point.

9. The system of claim 8, wherein, The position of the zero-stress anchor point is determined based on the following: calculating the variance or standard deviation of the ultrasonic wave propagation time of the measuring points in each set of homologous points; and screening one or more measuring points with the minimum variance or standard deviation as the candidate zero-stress anchor point.

10. The system of claim 9, wherein, Secondary verification of the zero residual stress is performed by manufacturing a corresponding zero residual stress calibration block at the candidate zero-stress anchor point.

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