The invention relates to nondestructive test methods for determining stiffness properties of plate structures. The invention relates more particularly to such methods employing propagation of acoustic waves through a plate structure of homogeneous or composite laminate form for determining Young""s modulus of the plate structure.
In a variety of mechanical or structural devices or assemblies, it is frequently desired to be able to determine changes in material properties of a given part, because such changes can be indicative of degradation of the part. For example, material stiffness is an important parameter affecting the performance of a structure. While structures are typically designed based on a known initial stiffness of the materials making up the structure, various factors can cause the materials to lose stiffness. Stress, fatigue, and environmental attack such as thermal and/or oxidation processes are just a few of the mechanisms by which a material can be degraded in terms of material stiffnes. Fiber/matrix composite materials are particularly susceptible to stiffness degradation, chiefly through a process known as micro-cracking in which microscopic cracks develop in the matrix material that binds the fibers together. Such micro-cracking can cause deleterious changes in mechanical properties, stress concentration, and redistribution within the composite material, which in turn can lead to performance degradation, delamination, and fiber damage. It is difficult, however, to detect micro-cracking using the types of nondestructive testing methods that heretofore have been available.
Prior to the present invention, there was no known nondestructive testing device suitable for use in the field, such as a hand-held device, for quantitatively determining changes in stiffness of a plate such as a composite laminate plate along an in-plane direction of the plate. The prior art teaches various methods for determining stiffness of isotropic materials using ultrasonic wave propagation through the material. For example, U.S. Pat. No. 5,741,971 to Lacy discloses a method for nondestructively measuring a Young""s modulus of a bulk isotropic material, such as cements or completion gels used in the petroleum industry for interzone isolation and fracture containment in drilling operations. The method involves using the through-transmission technique in which an ultrasonic transducer is disposed adjacent one end of a sample slug of the bulk material and another ultrasonic transducer is disposed adjacent an opposite end of the sample. The length of the sample between the two transducers is known. An ultrasonic pulse is generated by one of the transducers so as to cause an ultrasonic compression or longitudinal wave to be propagated beginning at one end of the sample, and the other transducer detects the wave when it arrives at the opposite end of the sample. The elapsed time between initiation of the wave at one end of the sample and arrival of the wave at the other end of the sample is measured. Based on this time and the known length of the sample, a velocity of the wave through the sample is calculated. A Young""s modulus for the material is then calculated based on the wave velocity and the known density and Poisson""s ratio of the material. The method of Lacy and the theory behind it are applicable only to isotropic materials. Lacy""s method requires placing transducers on two opposite sides of the sample, and thus would be difficult to apply to in-situ testing of a structure where it may be difficult or impossible to access both sides of the structure. Even if both sides of the structure could be accessed, the through-transmission technique of Lacy still cannot give a measurement of Young""s modulus in an in-plane direction, but can only provide an indication of stiffness in the thickness direction, which is the less interesting of the two directions.
U.S. Pat. No. 5,154,081 to Thompson et al. discloses a method for ultrasonic measurement of material properties for metal plates, involving using two transducers and a receiver arranged non-colinearly on one side of the plate. The two transducers generate Lamb waves that propagate along two different directions to the receiver. Based on differences in calculated velocities of the two Lamb waves, Thompson deduces material properties such as grain orientation and stress. The method is applicable only to metals, and does not provide a material stiffness measurement.
There has been a need, therefore, for a nondestructive method for measuring in-plane stiffness properties of plates including homogeneous isotropic plates and composite laminate plates. Additionally, there has been a need for such a method that can be used for in-situ examination of a plate where it may not be possible to access both sides of the plate.
The above needs are met and other advantages are achieved by the present invention, which provides a method for quantitatively evaluating in-plane stiffness properties of a plate in a nondestructive manner that is applicable to in-situ use, necessitating access to only one side of the plate. The method broadly comprises imparting energy to the plate at a first point located on a first of the major surfaces of the plate so as to cause an elastic wave to originate at the first point and propagate along the plate as a plate wave or guided wave. The plate wave generally consists of two wave modes, i.e., extensional and flexural wave modes. At a second point on the same surface of the plate and spaced from the first point along an in-plane direction, the extensional-mode wave, which travels faster than the flexural wave, is detected when it arrives. A velocity of the extensional wave along the in-plane direction of the plate is determined. Based on this velocity, a material stiffness of the plate along the in-plane direction is calculated.
The wave velocity can be determined by measuring the distance d between the first and second points and the elapsed time t required for the extensional-mode wave to travel the distance d from the first point to the second point, and dividing the distance d by the time t. Based on the velocity, a stiffness parameter for the plate along the in-plane direction is determined. The determination of the stiffness parameter is based on elastic wave propagation. The method can be applied to both homogeneous isotropic plates and composite laminate plate structures.
In accordance with a preferred embodiment of the invention applicable particularly to homogeneous isotropic plates, the stiffness parameter calculation in accordance with the invention comprises calculating the Young""s modulus based on the distance d and the time t. More particularly, the Young""s modulus E is calculated based on the equation
E=(1xe2x88x92xcexd2)xcfx81(d/t)2,
where xcexd is a predetermined Poisson""s ratio for the material of the plate and xcfx81 is a predetermined density of the material of the plate.
Preferably, the elastic wave is generated by applying acoustic energy to the plate. For example, a device for emitting acoustic pulses can be disposed against the plate surface and activated to create an acoustic pulse. An ultrasonic transducer or acoustic emission sensor can be used for this purpose. The extensional wave mode is detected with a second sensor placed a known distance from the first sensor against the same surface of the plate. It will thus be appreciated that unlike prior art methods employing the through-transmission technique in which a longitudinal wave is propagated from one side of a material to the other, the method of the invention is suitable for in-situ applications where it may not be possible or practical to locate sensors on both sides of the structure.
The methods described above are applicable primarily to isotropic plates and to quasi-isotropic composite laminate plates in which the plies are arranged in a lay-up such that the resulting laminate exhibits isotropic elastic behavior in the plane of the plate. The invention also provides a method for determining Young""s moduli of a composite laminate plate in the more general case of anisotropic laminates. This method involves solving a set of simultaneous equations to determine Young""s moduli for the plate along two orthogonal in-plane x- and y-directions corresponding to the zero-degree and 90-degree fiber directions of the laminate. The equations relate the Young""s moduli to the extensional wave velocities along these directions and to Poisson""s ratios and in-plane stiffness parameters for the plate. More specifically, one embodiment of the invention entails determining extensional wave velocities Cx and Cy along the x- and y-directions of a composite laminate plate, and solving the set of equations:
Cx={square root over (A11/xcfx81h)}xe2x80x83xe2x80x83Eq. (1)
Cy={square root over (A22/xcfx81h)}xe2x80x83xe2x80x83Eq. (2)
                              E          xx                =                                            σ              xx                                      ε              xx              xc2x0                                =                                                                      A                  11                                ⁢                                  A                  22                                            -                              A                12                2                                                    hA              22                                                          Eq.  (3)                                          v          xy                =                              -                                          ε                yy                xc2x0                                            ε                xx                xc2x0                                              =                                    A              12                                      A              22                                                          Eq.  (4)                                          E          yy                =                                                            A                11                            ⁢                              A                22                                      -                          A              12              2                                            hA            11                                              Eq.  (5)                                          v          yx                =                              A            12                                A            11                                              Eq.  (6)            
where h is the plate thickness, Aij (i, j=1 and 2) are the in-plane stiffnesses of the plate as defined in the composite laminate theory, xcfx81 is the plate density, and xcexdxy, and xcexdxy are Poisson""s ratios for the plate along the x- and y-directions. The plate density and Poisson""s ratios will generally be known or can readily be determined. Thus, these equations can be solved for the Young""s moduli. It can be shown, for quasi-isotropic composite plates, that this set of equations can be greatly simplified and reduced to the equation
E=(1xe2x88x92xcexd2)xcfx81(d/t)2
set forth above.
The invention also provides a method for quantitatively determining a change in Young""s modulus for a plate. The method comprises performing a first test in which energy is imparted to the plate at a first point located on the plate surface and detecting when the extensional-mode wave reaches a second point located on the same surface and spaced a predetermined distance from the first point, and measuring a first-elapsed time t1 required for the extensional-mode wave to travel from the first point to the second point. A second test is then performed in the same manner, making sure that the distance between the two points is the same as for the first test. A second elapsed time t2 required for the extensional-mode wave to travel between the two points is measured. A change in Young""s modulus for the plate is calculated based on a degree of difference, of the times t1 and t2. More particularly, it is assumed that the density and Poisson""s ratio for the material of the plate are constant or its change is negligible between the first test and the second test. A ratio of Young""s moduli for the first and second tests is calculated based on a ratio of the times t1 and t2. Advantageously, the ratio of Young""s moduli is calculated by the equation
E2/E1=(t1/t2)2,
where E1 is Young""s modulus for the first test and E2 is Young""s modulus for the second test. The first and second tests may be performed at two different times, in which case the change in Young""s modulus represents a change in material stiffness over time. Thus, the method of the invention can be used for periodic inspection as a way of monitoring the health of a structure. The information regarding changes in material stiffness can be used for prediction of remaining life of the structure or other purposes.