EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Materials Testing Machines Investigation of error sources and determination of measurement uncertainty G. Dahlberg; MTS Systems Corporation, Eden Prairie, USA
In an effort to meet National, International, and Commercial Accreditation requirements, users of Materials Testing Machines must establish adequate methods of determining calibration and test measurement uncertainties. Determining measurement uncertainty for testing machines and test data can be a very complex process. Many factors affect the uncertainty of test data produced by testing machines. This paper examines measurement uncertainty contributors associated with the calibration and use of modern materials testing machines. A list of uncertainty contributors is provided including examples of error source values and their assumed statistical distribution types. Methods of minimizing certain error sources are described. Also included, is a short section discussing measurement uncertainty related to ISO calibration practices ISO 376, Metallic materials – Calibration of force-proving instruments used for the verification of uniaxial testing machines and ISO 7500-1, Metallic materials – Verification of static uniaxial testing machines – Part 1: Tension/compression testing machines – Verification and calibration of the force-measuring system This paper discusses the effect of calibration uncertainties on test data produced by materials testing machines. Examples of how operators, materials, testing methods, and testing machine limitations, contribute to the measurement uncertainty of test data. One of two conditions will exist when testing materials or components. The material or component will either be under tested or over tested. There is simply no way to perform a materials test that contains zero error or has a zero value for the measurement
uncertainty. The task then is to identify as many sources of error as possible, and take measures to reduce or at least quantify, the resultant measurement uncertainty of data and or results produced by the material testing machine. Under testing a material or component may lead to safety, warranty, and liability problems due to premature failure or damage. This is of particular concern for the transportation and medical industries. Under testing conditions exist when the testing machine end level forces are not achieved and or the test speed, frequency, or cycle count is less than required to meet testing criteria. Over testing a material or component may lead to waste of time and material for design, fabrication, and test. Over testing is expensive and can potentially reduce competitive advantage. An over testing condition typically occurs when forces exceed the testing criteria. Under testing and over testing conditions can occur when acceleration induced forces are present, during transient cyclic overshoot of a start up waveform, when a testing machine is poorly controlled, or when the system is misadjusted or out of calibration status. So aside from regulatory accreditation pressures, currently being imposed on all areas of test and measurement, there are other excellent reasons for examining measurement uncertainty related to the operation of material testing machines. One common misconception and important point of interest, is that Testing Machine Manufacturers can provide total or combined measurement uncertainty values for material testing machines. This is simply not true and it would be unwise for manufacturers to provide these values. Testing Machine manufacturers design systems and software to perform specific tests under specified condi-
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EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
tions. Many specifications are published as optimal operating specifications. Few if any systems are operated under optimal conditions. Sources of measurement uncertainty should be assessed experimentally for each type of material, system configuration, and testing protocol to be performed. This paper concentrates on the indication and application of force when performing tests using material testing machines. The author acknowledges that material testing machines are used to apply and measure additional physical metrology parameters that may include but are not limited to displacement, torsional force, angular displacement, pressure, and strain. An uncertainty analysis pertaining to any metrologically significant parameter applied or measured, and reported by the testing machine should be assessed.
Major sources of measurement uncertainty can be grouped into the following categories. 1) Uncertainty due to the calibration equipment and calibration processes 2) Uncertainty of the Testing Machine as calibrated 3) Uncertainty of the Testing Machine during use 4) Uncertainty of the Test Results It must be understood that the uncertainty values presented in these examples are representative of a particular uncertainty analysis and do not represent all material testing machines of any specific type and or configuration. It should also be recognized that various interpretations related to error sources and their statistical contributions may vary depending on the method of analysis applied.
Static Calibration Uncertainty (1) ISO 10012-1: 1992(E), ISO 7500-1: 1999(E)
(2) ANSI/NCSL Z540-1,1997. Calibration – The set of operations, which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system, and the corresponding standard or known values derived from the standard.
(3) Standard Uncertainty express as one standard deviation or one sigma.
(4) Statistical Distribution. Reference ANSI/NCSL Z540-2-1997, NIS 3003 Edition 8, May 1995
(5) ISO 376, Metallic material – Calibration of force-proving instruments used for the verification of uniaxial testing machines, Table 2.
Calibration – The set of operations which establish, under specified conditions, the relationship between values indicated by a measuring instrument or measuring system, or values represented by a material measure or a reference material, and the corresponding values of a quantity realized by a reference standard.(1) (2)
provides information so that adequate adjustments can be made if required. Performing a calibration does not always require an adjustment. Uncertainty Static Calibration: Usc = v 0.052 + 0.252 + 0.042 + 0.022 + 0.022 = 0.26% (Root Sum Squared Method – RSS)
The term Calibration has often been associated with the act of making adjustments. When in fact the calibration process
Source Primary Force Calibration Force-Proving Device Long Term Drift of Calibration Device Environment Process Repeatability
Uncertainty (3) 0.05% Class 1 (5) 0.25% Class 1 0.04% 0.02% 0.02%
Distribution (4) normal normal rectangular rectangular normal
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Primary Force Proving Devices are calibrated in compliance with well documented practices. Although many countries have developed there own calibration/verification procedures, it is likely that most countries will soon adopt ISO 376 as a common guide when calibrating force-proving devices. Table 1, shows the parameters evaluated during an ISO 376 calibration and associated classification criteria. (6) I believe that most countries will also be adopting ISO 7500-1 as a guide when calibrating the static force indicating performance of the testing machine. Table 2, shows the measurement parameters and
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classification criteria for static force calibration of material testing machines.(7) Environment is an important parameter when calibrating testing machines. The temperature is very closely controlled in laboratories calibrating force-proving devices. ISO 376 requires that the laboratory temperature to be maintained with in ±1 ºC.(8) The calibration is to be performed with in a temperature range of 18 ºC to 28 ºC. Adequate time must also be allowed for the force-proving device to attain a stable temperature. This may take as long as an hour and can be assessed by monitoring the zero force indication.
(6) (7) (8)
ISO 376, Table 2. ISO 7500-1, Table 2. ISO 376, Section 6.4.3.
Characteristics of force-proving instruments of applied
Uncertaintyª
% Class
of reproducibility
of repeatability
of interpolation
of zero
of reversibility
calibration force %
00
0.05
0.025
±0.025
±0.012
0.07
±0.01
0.5
0.10
0.05
±0.05
±0.025
0.15
±0.02
1
0.20
0.10
±0.10
±0.05
0.30
±0.05
2
0.40
0.20
±0.20
±0.10
0.50
±0.10
ª The uncertainty of the calibration force is obtained by combining the random and systematic errors of the calibration force. Table 1
Characteristic values of the force-measuring system Class of Machine range
accuracy q
Maximum permissible value, % Relative error of repeatability reversibility b v
zero fo
Relative resolution a
0.5
±0.5
±0.5
±0.75
±0.05
0.25
1
±1.0
±1.0
±1.5
±0.1
0.5
2
±2.0
±2.0
±3.0
±0.2
1.0
3
±3.0
±3.0
±4.5
±0.3
1.5
Table 2
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(9)
ISO 7500-1, Section 6.4.2.
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
When these devices are used to calibrate material testing machines, the environment that the testing machine operates in can be quite different. ISO 7500-1 requires that the temperature during machine calibration not vary more than ±2 ºC.(9) The calibration of the testing machine shall be carried out at an ambient temperature between 10 ºC and 35 ºC. Most force proving devices have temperature compensation gauges or methods for calculating the reference calibration adjustment due to temperature. When using dead weights, the force must be compensated for the local value of gravity and air buoyancy. I have not found any evidence that humidity has an effect when performing calibrations of material testing systems. However, if force proving devices are not adequately sealed against humidity, extended time exposure to high humidity environments can cause bonding of force sensing gauges to degrade. Process Repeatability is determined experimentally by having a number of technicians perform calibrations with the same equipment. This can be done two ways. The technicians can use the calibration equipment to calibrate an artifact that simulates a system or the technicians can calibrate and actual testing machine. If the technicians calibrate a testing machine, some of the variance in the data will be due to the testing machine itself. This is difficult to assess. Automated calibration systems help reduce the variance due to process repeatability.
I have not included Alignment as one of the uncertainty contributors related to calibration. Calibration technicians are normally trained to ensure proper axial alignment when doing calibrations. Most systems would be difficult to fixture if alignment were in such a condition that the calibration data would be significantly affected. The forceproving device is rotated and data is acquired during calibration. The force-proving device’s sensitivity to a normally experienced out of alignment condition is included in the combined uncertainty for the device. This is why fixtures and studs used with force-proving devices, should be used when forceproving devices are being calibrated. I did however experience a rare situation while calibrating a universal testing machine. This was a testing machine in which the system force transducer is physically moved when switching from Tension to Compression mode or the reverse. An amount of dirt and debris present on the mating surface between the system crosshead and force transducer caused an out of alignment condition resulting in a 2% shift in the sensitivity of the force indication device. Therefore it is important to inspect these mating surfaces prior to performing a calibration. Many quality control programs require that «As-Found» calibration data be obtained prior to making any changes to a testing machine. This is good metrology practice and can provide confidence in data and tests performed between calibration intervals. On the other hand this practice can also uncover evidence that materials or components have been incorrectly tested. If As-Found calibration data is required, calibration data must be recorded prior to cleaning or changing the condition of the machine.
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
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Static Testing Machine Uncertainty Source Resolution Uncorrected Error
Uncertainty Static Testing Machine: Ustm = v 0.22 + 0.22 = 0.28% Resolution is often defined as one half the noise, with the lowest calibration force applied, or one digit of a digital display, whichever is greater.(10) Uncorrected Error is the amount of error from the static calibration of the testing machine. This amount of error could be equal to the maximum value of the error allowable specific to the required Testing Machine Classification. I have chosen 0.2% because this is normally the largest amount of error we would leave when recalibrating a Class 1 type, testing machine. This value may be as large as ±1.0% for a Class 1 machine. Repeatability is included in the estimate for Uncorrected Error. Repeatability may be treated separately depending on the calibration or evaluation procedures used. So far we have examined uncertainty contributors related only to the static calibration and static performance of the testing machine. This is an important point. Often this is where the uncertainty analysis ends. Currently accepted Material Testing Machine calibration /verification procedures(11) allow for the calibration of the system at low forces with certified deadweights. This essentially means that the force applying apparatus of the testing system need not be turned on or running during the calibration. This will provide for very stable and repeatable calibration data, but will not reflect any real world application. The problem is that very few real world tests are purely static in nature. It is my opinion that most tests performed with mod-
Uncertainty 0.20% 0.20%
Distribution rectangular rectangular
ern Material Testing Machines are dynamic to a certain degree. Tests that utilize deadweights for simple proof testing, are the exception. Most modern material testing machines provide for some type of closed loop control of the machine. Simply described, closed loop means that a signal from one of the system’s calibrated transducers is fed back into the system’s control circuit to automatically re-adjust the system to maintain desired levels of force and or displacement. System performance is greatly influenced by many factors related to closed loop operation. This process is occurring continually during a test. Therefore, the changing physical parameters being applied to the specimen as the specimen’s physical characteristics change cause the system to react producing a dynamic response. Does this mean that in order to have a defined level of confidence in the data produced for any test requires a dynamic calibration or verification? Possibly. But before anyone should under take such an involved task, there are a number of other things that should be investigated.
Testing Machine Uncertainty During Use The measurement uncertainty contributors in the section have the potential of making all calibration sources of measurement uncertainty insignificant. Keep in mind that sources of uncertainty are combined in the RSS method. This results in added weight for the major contributors. A material testing machine ill suited for a particular test can
(10) ASTM E4-99, Standard Practices for Force Verification of Testing Machines, Sections 3.1.12, 3.1.13.
(11) ISO 7500-1 Section 6.1, ASTM E4-99 Section 1.1.
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EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
contribute errors in force measurement and application well in excess of all other combined uncertainties related to the testing machine’s use. I do not have data to provide representative uncertainty values for all listed error
sources. I have designated those error sources for which I have no objective evidence as Not Available (N/A). Uncertainty Testing Machine During Use: Utmdu = v0.042 + 0.12 + 0.52 + 0.12 + 0.012 + 0.12 = 0.53%
Force Measuring and Application System Effects Source Drift Noise Resolution Stability (servo-hydraulic supply) Backlash (electro-mechanical)
Uncertainty .04% .1% .5% N/A .1%
Distribution rectangular rectangular rectangular
Uncertainty .01% N/A
Distribution rectangular
Uncertainty N/A N/A
Distribution
Uncertainty .1% N/A .5% .2% to > 10%
Distribution rectangular
rectangular
Environment Source Temperature Power Fluctuations
Specimen Alignment Source Testing Machine and Grips Damage to the machine
Application and Procedural Errors Source Errors due to system zeroing Specimen preparation Errors in reading displays Test Speed
(12)
NIS 3003 Edition 8 May 1995, ANSI/NCSL Z540-2-1997
I have not included the uncertainty contribution values for Errors in reading displays or for Test Speed because I have included a fairly large value for resolution. Depending on the type of evaluation and testing being performed, one of the other sources of resolution error may become the dominate contributor resulting in a value less than or greater than 0.5%.
normal rectangular
The combined Testing Machine uncertainty can be expressed: CUtm = v Usc2 + Ustm2 + Utmdu2 or CUtm = v 0.262 + 0.282 + 0.532 = 0.65% Expanded Testing Machine Uncertainty (k = 2) (12) can be expressed: EUtm = 2 x CUtm or 2 x 0.65 = 1.3% for a confidence level of 95%
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Force Measuring and Application System Effects Drift during use can be related to the system’s inability to control well. The system may need to wonder off the target force by a relatively large amount before the control signal makes an adjustment to correct the system. Drift can also occur due to system devices changing relative to temperature. Creep in the system’s force transducer can add to this uncertainty value as well. Noise can occur in the form of mechanical noise, electrical noise, or both. Mechanical noise to some degree is almost always present when the system is running. In modern well designed and controlled systems operating with in normal operating ranges of measurement and control, the total noise due to electrical and mechanical influences may be ±0.1% or less. Resolution error can be due to noise, data acquisition capabilities, and or test speed. If resolution is evaluated as a factor of noise during test, the uncertainty contributor for resolution determined from the static calibration analysis need not be summed in the total combined uncertainty value. See Test Speed below for additional explanation. Stability can be affected by the number of servo-hydraulic systems on a single hydraulic supply. It is fairly easy to know when the pump does not have enough flow or pressure to produce the end level forces required. But it is not so easy to assess what happens to the specimen or system when running long tests and numerous machines on the same supply are starting and stopping tests. The only way to know the effect is to experimentally test this condition. I have not included an uncertainty contribution value because it is highly subject to the type of testing and type of specimen /component being tested. Ideally, there would be one testing machine per supply or only one machine would be running at one time. This
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may not be economically feasible so it is an area of potential error that should be investigated. Backlash in electro-mechanically driven testing machines can influence testing results. The amount of backlash present can be assessed during calibration. Backlash can also be minimized by causing the crosshead to advance past the point in which the test is to be started and then adjusted to the start point of the test in the intended direction of the test. This is a procedural issue and is only effective for unidirectional tests. If automated bi-directional or cyclic testing is to be performed with these types of machines, the uncertainty contribution should be determined and include in the combined measurement uncertainty.
Environment Temperature during a test may be significantly different than the temperature during calibration. An evaluation of the effect of this difference should be performed. Where applicable, test results may be corrected due to temperature differences. Temperature changes during the test may also affect the test results. These gradients should be known and included in the uncertainty analysis. A typical load cell temperature coefficients specification.(13) Effect on Output - %/ºC Maximum: ±0.0015 Effect on Zero - %RO/ºC Maximum: ±0.0015 We have found in our testing that as long as the load cell temperature remains at or very near to the temperature at which the test is started, the error due to the temperature being significantly different than the temperature at the time of calibration is minimal. Because the system load cell is normally zeroed at the beginning of a test, if the temperature then changes during the test,
(13) Interface, Inc. 1200 series load cell specifications, 2000 product catalog
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EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
this is when the system force device will contain errors when indicating force. I have included an amount of uncertainty for this contributor that would reflect a 5 ºC change in temperature from the start of a test. Power fluctuations may affect testing machine operation and data integrity. If the power source meets recommended manufacturer’s specifications, no value for measurement uncertainty need be included for this condition.
Specimen Alignment Good specimen alignment can be critical to the life of the specimen being tested and thus important to the data characterizing a particular material property. Testing Machines and Grips are manufactured to apply and maintain good alignment. Again, it is difficult to put an uncertainty value to this contributor because the value would be only significant for a specific type of specimen and test. Some manufacturers produce alignment devices that are easy to use and can be adjusted with force applied. I have found these to work well when good alignment is critical. Damage to the machine can occur at any time. Inspection of the system is critical to maintaining operational performance. A damaged machine can induce an out of alignment condition. Poorly maintained systems can lead to seal friction problems, which can result in loss of hydraulic pressure and oil leakage during cyclic testing. ServoHydraulic systems require a clean oil supply in order to operate optimally. Most manufacturers will offer oil sample testing. Poorly maintained or damaged electro-mechanical testing machines may have excessive gear play and or drive belts that are stretched. This can cause excessive backlash and start up lag times. Assigning a value for measurement uncertainty due to machine wear and or damage is difficult.
With all potential sources of measurement uncertainty in this section thus far, round robin testing between different testing machines and if possible between different laboratories using adequate reference materials can provide evidence that the combined measurement uncertainty due to these contributors are minimized and with in adequate control limits.
Application and Procedural Errors These sources of measurement uncertainty have the potential to be the most significant sources of errors when performing tests on materials and or components. These sources of measurement uncertainty are also the most commonly overlooked sources when performing an uncertainty analysis. Common data acquisition zeroing errors can occur when the test operator arbitrarily zeros the data acquisition system at the start of a test. Careful attention and an understanding of the test conditions and testing system configurations are important or significant offsets in the resultant data can be induced. This source of measurement uncertainty is specific to the test and can have a wide range of values. Fixturing, preloading, and backlash can have an effect on this component. I have included a value for measurement uncertainty equal to the amount commonly experienced when the system is not zeroed after performing initial hysteresis cycling or if hysteresis cycling is not performed. Specimen preparation is critical to repeatable and predictable results. It is my experience that most testing laboratories do a good job of following established procedures when fabricating and preparing specimens. But, even relatively small dimensional machining errors can cause large errors in specimen performance. Again this is a difficult measurement uncertainty source to quantify. Lot testing can often uncover problems of this type.
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Test Speed The largest errors I have experienced related to the testing of materials and or components have been due to inappropriate application of the testing machine. Testing machines are expensive and it is not unrealistic to expect users of testing machines to use their systems for as many different types of tests as possible. Many times the system’s limitations are not well understood. Here is an example of a real world situation I was involved in. A testing laboratory designed a test protocol to test a polycarbonate component used in the medical industry. The test engineers wanted to simulate a patient’s instantaneous arm movement, such as a convulsion or involuntary muscle reaction. This movement would result in applying force to the component attached to the patient via intravenous tubes. A Tensile Pull Test was designed to determine the force at which the polycarbonate component would break under such conditions. A minimum force was required to validate the component for continued production. The test protocol was performed for validation of design as well as for continued production. Manufactured samples were brought in periodically for lot qualification testing. The test was designed to run on an electro-mechanical material testing machine. The system was selected to move the crosshead at 20 inches/minute. The specimen to be tested was fixtured so that there was zero
pre-travel before force was applied. The brittle nature of the polycarbonate specimen resulted in a test duration that lasted only 0.2 second. There were two basic problems with this test. The test engineer assumed that the crosshead would be moving at the expected speed when the failure occurred. Specimen failure was defined as the peak force at which the component physically came apart.
Crosshead Speed Ramp 20
Speed (in./min)
Errors in reading displays are quickly becoming a small source of measurement uncertainty due to modern computer controlled testing machines. I still on occasion have situations where the customers are trying to determine a force or data point on a stress-strain curve below the first one inch increment on a 10 inch chart recorder. Often times the potential error related to this practice is neither assessed nor included in an uncertainty analysis. Errors can easily equal ± 0.5%.
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15 10 5 0 0
5
45
85
125
165
225
milliseconds
The graph shows that the crosshead was moving at approximately 16 inches/minute just prior to specimen failure. The customer’s test protocol specified that the test speed have a tolerance of ±5% of desired speed. The graph shows that the speed at specimen failure was 20% below the test criteria. The second mistake was to assume that the testing machine’s data acquisition system was adequate to capture the force indication at the time of specimen failure. The customer expected that the error of peak force indication would be no greater than ±5%. This was also not the case. Table 3, shows the data acquired just prior to specimen failure.
Force (N)
Graph 1 – Testing Machine Crosshead Speed
Table 3 – Date Acquired from Tensile Pull Test of Polycarbonate specimen at 20 inches/minute
∆ Force (N)
%
2106
187
8.9
2301
195
8.5
2507
206
8.5
1919
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EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
By examining the data shown in Table 3, a couple of important things are apparent. The data in the ∆ Force (N) column shows the difference in force between sequentially acquired data points. The difference between the first two data points is 187 N and the force between the last two data points prior it specimen failure is 206 N. Because the force is increasing between each acquired data point, we know that the crosshead is still accelerating to the desired test speed. The next data point if the specimen had not failed would likely have been approximately 216 N or 8.6% from the previous data point. The system reported the specimen failure at 2507 N. The specimen could have failed anywhere with in an 8.6% window greater than 2507 N. Data from the reference device used to prove these findings recorded an average error in the reported peak force at failure of -7.22% with a maximum error recorded at -19.47%. This was based on a population of 60 tested samples.
data fast enough. Few systems are capable of sample rates sufficient to meet the requirements of this testing protocol. The best way to run this test and acquire data with in the accuracy desired is to simply slow the test down. When the test was slowed to 2 inches/minute the data acquired averaged -0.43% with a maximum error of -1.22% based on 12 tested samples. This of course would not provide the instantaneous movement the design engineers had originally wanted to simulate.
It is important to note that this test resulted in errors that where conservative in nature. The actual peak forces required to cause the specimen to fail were much greater than the test results would indicate. Therefore related to safety and liability this was an overly safe test.
An interesting side note to this scenario is that the customer would probably never have become aware of this problem if they had not purchased a new machine for testing in the laboratory. They planned to run the same tests on both machines to increase testing efficiency and found that the new machine produced data quite different than their older machine. While I was there, I tested their older machine as well and found that the results from that machine were considerably worse than the new machine. We determined that the older machine was sampling at 50 samples per second where as the new machine was sampling at 200 samples per second. Errors in peak force indication for the older machine averaged -35% with a maximum error of -45%. Neither machine was sampling fast enough to produce data with in the desire specification.
This system was not capable of performing the test with in the expected design specifications. There are a couple of things that could have been done in order to run this test closer to the design criteria. In order for the crosshead to be moving at the desired speed when the event occurs, the system needs sufficient time to overcome ramp up conditions. This could be accomplished by designing fixtures that let the crosshead move a distance prior to the application of force on the specimen. In order to acquire test data with in the desired ±5% specification, the system’s data acquisition system would need to sample much faster. The system had sufficient static resolution but dynamically it could not acquire
The equipment used to validate the testing protocol consisted of a certified traceable high-speed data acquisition system capable of 100,000 samples per second with 16 bits of resolution. The data acquisition system was connected to a certified force-proving device fixtured in the load train during the test. I wrote custom software to use with the system in order to acquire and present the results.
EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Uncertainty of Test Results
Recommendations
One method of determining the uncertainty of test results is to obtain the standard deviation of a series of tests performed with one particular set of control samples (Ucsr) on the same machine. The standard uncertainty will include data scatter attributed to the samples. If reference material samples are available, tests can be run and the standard deviation derived (Urmsr). These values are very dependent on the type of materials and tests performed. The range of values can easily range from 0.1% to 1.0% and greater. For the purpose of this exercise I will assign 1.0% to Ucsr and 0.5% to Urmsr.
These recommendations are intended to minimize measurement uncertainty and provide increased confidence in data produced by material testing machines.
The combined measurement uncertainty for the testing machine and testing results can be derived. Combined Uncertainty of Testing Results: CUtr = v Usc2 + Ustm2 + Utmdu2 + Ucsr2 - Urmsr2 CUtr = v 0.262 + 0.282 + 0.532 + 1.02 - 0.52 = 1.08% Expanded Uncertainty for the Test Results (k = 2)(14): EUtr = 2 x CUtr = 2.16% for a confidence level of 95% Note: I have not included any value for the uncertainty due to errors induced by acceleration, system resonance, or other dynamically induced error sources. It is not recommended that tests be performed when dynamically induce errors are present. An evaluation of dynamically induced error sources is beyond the scope of this paper.
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1.) Once an uncertainty analysis is complete, concentrate on reducing major sources of measurement uncertainty. 2.) Know your testing machine’s capabilities. Design your tests to operate with in the testing machine’s capabilities. Verify experimentally that all testing protocols are operating with in expected specifications. 3.) Examine the raw test data from your tests. Verify that the system is reporting the correct results from the raw data. 4.) Test reference materials in a number of machines and compare results between machines. Participate in round robin testing of reference materials between different laboratories. 5.) Keep the testing machine in optimal operating condition. Have your testing machine on a scheduled maintenance program and have it serviced by trained individuals. 6.) Keep your testing machine in a calibrated condition. Shorten calibration intervals based on historical calibration results where applicable.
(14) NIS 3003, ANSI/NCSL Z540-2-1997
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EUROLAB International Workshop: Investigation and Verification of Materials Testing Machines
Bibliography [1]
[2]
[3]
[4]
ISO 10012-1: 1992 (E), Quality assurance requirements for measuring equipment – Part 1: Metrological confirmation system for measuring equipment.
[5]
ANSI/NCSL Z540-2-1997, U.S. Guide to the Expression of Uncertainty in Measurement.
[6]
ASTM E74-00a, Standard Practice of Calibration of Force-Measuring Instruments for Verifying the Force Indication of Testing Machines. ASTM Volume 03.01.
[7]
ASTM E4-99, Standard Practices for Force Verification of Testing Machines. ASTM Volume 03.01.
[8]
EAL-G22, Uncertainty of Calibration Results in Force Measurements
[9]
Interface, Inc. Product Catalog 2000.
ISO 376: 1999 (E), Metallic materials – Calibration of force-proving instruments used for the verification of uniaxial testing machines. ISO 7500-1: 1999 (E), Metallic materials – Verification of static uniaxial testing machines – Part 1: Tension/compression testing machines – Verification and calibration of the force-measuring system. NIS 3003 Edition 8: May 1995, The Expression of Uncertainty and Confidence in Measurement for Calibrations.
