Evaluation of measurement uncertainty of drop hammer impact test for composite materials

Future aircraft structures are usually dominated by composites, and one of the key defects and forms of damage to composite structures is the impact damage caused by low-energy (especially low-speed) foreign matter. This kind of low-energy impact test is usually completed by the drop hammer testing machine, so accurately assessing the impact test of the falling hammer completed in accordance with the standard test method, and the reliability of the permissible value of the impact performance of the objective reaction composite is of great significance to the future aircraft structure design. Taking a standard composite test piece as an example, considering the key factors in the whole process of impact test, a mathematical model is constructed, and the measurement uncertainty of different configuration composite test pieces of different configurations is calculated according to the test data, which provides a basis for aircraft structural design.


Introduction
Future aircraft structures are usually dominated by composite materials.And one of the key defects and damage forms of composite structures is impact damage caused by low-energy (especially low-speed) foreign objects [1][2] .This low-energy impact test is usually performed by a drop-weight testing machine.The allowable value of composite impact performance obtained by the drop weight testing machine is an important reference index for aircraft structural design, so it is very important to accurately obtain the allowable value of composite impact performance through testing.The accuracy of the impact test measurement results is closely related to the measurement method and measurement equipment, and the correct evaluation of its uncertainty can compare the reliability of the allowable value of composite impact performance objectively, which is of great significance to future aircraft structure design.
Zhang Xiaojuan and Zhang Boping from Northwestern Polytechnical University have made useful explorations on the relationship between impact energy and pit depth and gave the corresponding reference formula [3][4] , and Serge Abrate from Southern Illinois University in the United States also gave the relationship between impact force and pit depth according to Hertz's contact law [5] .
In this paper, the process of testing the uncertainty of the system by a specific impact test is used to check the accuracy of the allowable value of the impact performance of the composite material and reduce the evaluation workload and improve the accuracy.

Experiments and calculations
The impact resistance of composite materials is evaluated according to JJF1059.1-2012 "Evaluation and Representation of Measurement Uncertainty" [6] . 1) Test method.According to ASTM D7136 "Standard Test Method for Measuring the Damage Impedance of Fiber Reinforced Polymer Matrix Composites to Drop Weight Impact Events".
2) Environmental conditions.The test method requires a room temperature of 10 ºC ~ 35 ºC and relative humidity ≤ 85%.The room temperature of this test was 20 ºC and the humidity was 79%.
4) Test piece.The test piece is made of medium-mold high-strength carbon fiber reinforced M21C epoxy resin unidirectional with prepreg, the material specification is CMS-CP-309: Type 34, Class 3, Class 194, grade M21C/34%/UD194/IMA/6.4-3, and the nominal thickness of the single layer of the laminate after curing is 0.187 mm.All test pieces mentioned in this document are manufactured using automatic wire laying and autoclave curing auxiliary processes.The padding used for the test is shown in Table 1, and the test piece configuration and testing machine are shown in Figure 1.

Sources of uncertainty and mathematical models
The working principle of the drop weight impact test is to lift the corresponding mass of the heavy hammer to a certain height, do free fall movement, convert the gravitational potential energy of the drop weight into kinetic energy, and impact the test piece at a certain speed, so as to verify the impact resistance of the test piece, the test piece is washed out of a certain pit, and there is a certain relationship between the impact energy and the depth of the pit.The uncertainty of the impact test results includes 1. the uncertainty introduced by repeated measurements and 2. the uncertainty introduced by the test equipment.Among them, there are two main parameters for repeated measurement: 1. the impact energy of the drop weight; 2. the pit depth of the test piece.
Most researchers use Hertz's contact law [7] to model local deformation, according to Hertz's contact law, the impact force F of the drop weight tester is related to the ɑ of indentation depth as follows: F=k  (1) The impact energy can be determined using the functional principle, and the work done by the impact force during the indentation from 0 to the maximum pit depth is: In Equation ( 2), Ec is the impact energy (J); m is the mass of the drop weight (kg); g is the acceleration due to gravity (m/s 2 ); h is the drop weight impact height (m); kc is the contact stiffness, which is related to the material properties of the impactor and the impacted object, and α is the depth of the pit caused by the impact of the drop weight.
The contact stiffness kc is as follows: R and E in Equation ( 3) are derived from the following equation: R1 and R2 are the radius of curvature (mm) of the impact head and the impacted object, E1 and E2 are the elastic modulus (Gpa) of the impact head and the impacted object, and μ1 and μ2 are the Poisson's ratio between the impact head and the impacted object.
The impact energy and pit depth required to generate 1mm pits with different test piece configurations are shown in Table 2 below.

Measurement uncertainty component introduced by experimental repeatability
The measurement uncertainty component introduced by experimental repeatability was evaluated using class A standard [8][9] .Repeated observations of the same measured independently n times under repeatability conditions yielded n measured values, the arithmetic mean is calculated, and we use Bezier's formula to calculate the measured class A standard uncertainty A u . 1 In Equations ( 6)-( 8):  -the arithmetic mean of the pit depth.'  -the deviation value of the pit depth.n -Number of valid specimens.
In Equations ( 9)-( 10): E -the arithmetic mean of the impact energy.n -Number of valid specimens.
According to the test data in Table 2, we substitute Equations ( 6) ~ ( 11) to obtain Table 3.

The uncertainty component introduced by the test equipment
The uncertainty introduced by the metrological performance of the measuring instrument: In Equation ( 12

Synthetic standard uncertainty and extended uncertainty
The synthetic uncertainty for measuring the damage impedance of fiber-reinforced polymer matrix composites to drop weight impact events is: The extended uncertainty U is equal to the product of the synthetic standard uncertainty c u and the inclusion factor k [10][11] .
The inclusion factor k is related to the measured σ distribution.In general, k = 2, substituting the data, we obtain the extended uncertainty values of different composite configurations with a 95% confidence probability, as shown in Table 4 below.

Conclusion
It can be seen from the test data that in the impact test of composite materials, even composite materials of the same thickness, the same size, and different layers have different measurement uncertainties.Parameter repeatability measurement, drop weight and other test equipment have an impact on the results, repeated measurement caused by the error has the greatest impact on the uncertainty of the results, so the test process should be strictly in accordance with the standard test.Especially the part where people participate, need multiple measurements to improve the measurement accuracy.

Table 1
List of laminate lay-up for pit test of damage characteristics of composite fuselage.

Table 2
Drop weight testing machine test data.

Table 3
Repeated measurement of uncertain components. ):

Table 4
Synthetic uncertainty and extended uncertainty.