Method for reconstructing crack profiles based on composite-mode total focusing method

A method for reconstructing crack profiles based on a composite-mode total focusing method, wherein

• a detection system comprising an ultrasonic phased array device, a phased array probe, and an angle wedge is adopted to acquire A-scan signal matrix;
• based on Fermat's principle, refracted points of ultrasonic waves at an interface between a wedge and a sample are calculated to obtain a corresponding amplitude for each view in a region of interest;
• for each reconstructed point, a view having a strongest response is selected from 21 views;
• the crack profiles corresponding to different orientation angles are reconstructed by delay-and-sum beamforming;
• and
• the method comprises the following steps:
• (a) selection of parameters for detection, comprising:
• selecting parameters for detection according to a material, a shape, and a size of a to-be-measured sample, where the parameters comprise:
• a frequency of an ultrasonic phased array probe, the number of array elements, and a wedge angle;
• (b) acquisition of an A-scan signal matrix, comprising:
• acquiring the A-scan signal matrix comprising different views at one time by using a full matrix capture function of the ultrasonic phased array device, based on selected parameters for ultrasonic testing, and saving the A-scan signal matrix in a txt format, in which, for an ultrasonic phased array probe having n elements, the number of the A-scan signals in matrix is n2;
• (c) establishment of a coordinate system and grid division of the region of interest, comprising:
• establishing the coordinate system by defining the interface between the wedge and the sample as an x-axis, defining a projection point from a center position of a first element of the phased array probe to the x-axis as a coordinate origin, defining a direction of a leading edge of the wedge as a positive direction of the x-axis, and defining a depth direction of the sample as a positive direction of a y-axis;
• and dividing the region of interest into M×N rectangular grids, wherein grid nodes are image reconstruction points;
• (d) determination of wave modes, comprising:
• classifying the wave modes as three types according to different propagation paths of ultrasonic beams, where the three types of wave modes comprise:
• a direct mode, where the ultrasonic beam is emitted by one element, interacts with a crack, and is directly received by array element;
• a half-skip mode, where the ultrasonic beam is emitted by one element and reflected by a bottom of the to-be-measured sample, interacts with the crack, and is received by array element;
• and
• a full-skip mode, where the ultrasonic beam is emitted by one element and reflected by the bottom of the to-be-measured sample, interacts with the crack, is reflected by the bottom of the sample, and is received by array element;
• and
• mode conversion occurs at the interface between the wedge and the sample, the bottom of the sample, and the crack surface, so the three types of wave modes are divided into 21 views, which contain 3 views in direct mode (LL, TT, and LT, where L for longitudinal wave and T for transverse wave), 8 views in half-skip mode (TLT, LLT, TTT, LTT, LLL, TLL, TTL, and LTL), and 10 views in full-skip mode (LLLL, TTTT, LLLT, LLTT, LLTL, LTLT, TLTT, TLTL, LTTT, and LTTL);
• (e) solving positions of refracted points, comprising:
• defining abscissas of the refracted points at the interface between the wedge and the sample for the emitted and received signals in view p as xpi and xpj, respectively;
• establishing equation (1) according to the Fermat's principle:
• ∂
• t
• pi
• ∂
• x
• pi
• =
• ∂
• t
• pj
• ∂
• x
• pj
• =
• 0
• ,
• (
• 1
• )
• wherein 1≤p≤21, tpi is travel time of an ultrasonic beam excited from i-th element and to the reconstruction point, and tpj is travel time of the ultrasonic beam from the reconstruction point to j-th element, where 1≤i≤n and 1≤j≤n;
• and
• calculating tpi and tpj according to ray paths of the ultrasonic beams and the wave modes;
• (f) image reconstruction by the composite-mode total focusing method, comprising:
• for each reconstruction point (a, b) in the region of interest, where 1≤a≤M, 1≤b≤N, selecting a strongest response from the 21 views for the signal Aij transmitted by the i-th element and received by the j-th element as a corresponding reconstruction amplitude Iij(a, b):
• I
• ij
• ⁡
• (
• a
• ,
• b
• )
• =
• max
• 1
• ≤
• p
• ≤
• 21
• ⁢
• (
• A
• ij
• ⁡
• (
• t
• p
• ⁡
• (
• a
• ,
• b
• )
• )
• )
• ,
• (
• 2
• )
• in which, tp(a, b) is a travel time following the path of a p-th view via the reconstruction point (a, b);
• repeating the above steps point by point in the region of interest to obtain the reconstructed image by the composite-mode total focusing method, where the composite delay-and-sum amplitude I(a, b) of the image reconstruction point (a, b) is:
• I
• ⁡
• (
• a
• ,
• b
• )
• =
• ∑
• i
• =
• 1
• n
• ⁢
• ⁢
• ∑
• j
• =
• 1
• n
• ⁢
• ⁢
• I
• ij
• ⁡
• (
• a
• ,
• b
• )
• ;
• (
• 3
• )
• and
• (g) quantification, positioning, and orientation of cracks, comprising:
• using −6 dB drop rule to obtain depths, lengths, and inclined angles of the cracks with different orientation angles according to the composite-mode total focusing image.