Method for calculating hull structure crack propagation length based on stress monitoring

Abstract

The invention relates to the field of fracture mechanics, in particular to a hull structure crack propagation length calculation method based on stress monitoring, which comprises the following steps: S1, determining a stress monitoring area in a crack propagation process; s2, selecting a measuring point in the stress monitoring area, and acquiring a stress component time calendar and a strain component time calendar of the measuring point; S3, calculating a crack tip stress intensity factor time calendar; s4, on the basis of the stress intensity factor time calendar obtained in the step S3, the crack propagation length is calculated through a Paris formula; through the stress intensity factor range near the crack tip, the crack propagation length of the local structure can be simply and rapidly calculated through a rain flow counting method, a solution is provided for crack propagation prediction research of large components such as a hull structure, and a reference is provided for hull structure safety. The method is easy to implement, high in calculation precision, high in efficiency and high in operability.

Description

Technical Field

[0001] The invention relates to the field of fracture mechanics, and in particular to a method for calculating the crack extension length of a hull structure based on stress monitoring. Background Art

[0002] During the welding process of large engineering structures, due to inevitable microscopic and macroscopic defects, these defects are very likely to develop into surface cracks that are approximately semi-elliptical under various alternating loads, especially at the weld toe where stress concentration is more serious. Under continuous external loads, surface cracks will gradually expand and penetrate the steel plate to form through cracks. However, since engineering structures usually have a high degree of redundancy, the appearance of surface cracks or even through cracks does not necessarily lead to immediate damage to the cracked area, but when the crack length expands to a certain size, it will significantly affect the safety of the structure and may cause structural failure.

[0003] In order to predict the propagation behavior of cracks in structures, the range of stress intensity factors near the crack tip of the structure is often used for calculation. Stress intensity factor is an important mechanical parameter that reflects the singularity of the crack tip and is of great significance in fracture mechanics. It is widely used to assess the safety of the residual strength of structures, estimate life, analyze failures, and measure the fracture toughness of materials. The crack growth rate is not only closely related to the material parameters, but also directly related to the range of stress intensity factors. The larger the range of stress intensity factors, the higher the amplitude of the cyclic load borne by the structure, which leads to a faster crack growth rate and a longer crack growth length within a certain number of loading cycles.

[0004] At present, most studies focus on the crack growth behavior in small simple structures, while there are relatively few studies on crack growth in large engineering structures such as ship hulls, especially in monitoring the local crack growth length of large structures. This limitation brings challenges to the crack growth monitoring and prediction of large structures, and restricts the in-depth understanding and optimization of their fracture behavior. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for calculating the crack propagation length of a hull structure based on stress monitoring, which can calculate the stress intensity factor history of the crack tip according to the stress and strain components of the measuring points near the crack tip, and obtain the crack propagation length of the structure using the stress intensity factor history.

[0006] The present invention provides a method for calculating the crack propagation length of a hull structure based on stress monitoring, comprising the following steps:

[0007] S1. Determine the stress monitoring area during crack propagation;

[0008] S2, selecting a measuring point in the stress monitoring area, and obtaining a stress component time history and a strain component time history of the measuring point;

[0009] S3, calculate the crack tip stress intensity factor time history;

[0010] S4. Based on the stress intensity factor history obtained in step S3, the crack extension length is calculated using the Paris formula.

[0011] This technical solution can simply and quickly calculate the local structural crack extension length through the range of stress intensity factors near the crack tip by using the rain flow counting method, providing a solution for crack extension prediction research of large components such as hull structures, and providing a reference for the structural safety of the hull. This method is easy to implement, has high calculation accuracy, high efficiency and high operability.

[0012] In some embodiments of the present application, in step S1, a rectangular area that can contain the crack tip is selected as the initial stress monitoring area D 0 , when the crack extends beyond the initial stress monitoring area D 0 When the range is , the initial stress monitoring area D is monitored according to the direction of the crack extension. 0 Extend and adjust to form a new rectangular stress monitoring area D i (i=1, 2, 3, ...), so that in the process of the crack extending from the length to be monitored to the dangerous length, the crack is in the initial stress monitoring area D 0 or the stress monitoring area D i within the range.

[0013] In some embodiments of the present application, the initial stress monitoring area D 0 The four vertex positions of are measuring points, and monitoring equipment is arranged on the measuring points, and the monitoring equipment is used to measure the stress component time history and strain component time history around the crack tip during the crack extension process;

[0014] As the crack expands, the stress monitoring area D is formed. i When , the position of the measuring point also changes to the stress monitoring area D i The monitoring device is transferred to the stress monitoring area D i on the measuring point.

[0015] In some embodiments of the present application, in order to prevent the crack from extending too fast and causing the monitoring equipment to be arranged in time, resulting in the loss of data and affecting the subsequent crack extension length calculation, multiple stress monitoring areas D can be defined in advance in step S2. i , and in the stress monitoring area D i The monitoring equipment is deployed at the measuring points.

[0016] In some embodiments of the present application, the monitoring device is connected to a data collector, and the data collector is used to collect the stress component time history data and the strain component time history data monitored by the monitoring device at the measuring point position.

[0017] In some embodiments, the specific steps of calculating the crack tip stress intensity factor history in step S3 include:

[0018]

[0019] Where I is the path-independent integral, which represents the energy release rate at the crack tip;

[0020] Γ is a curve around the crack tip;

[0021] ω is the strain energy density; T x , T y is the component force acting on the unit length of the integrating loop;

[0022] u x ,u y is the displacement component; ds is the integral arc length;

[0023] Among them, T x , T y The following conditions must be met:

[0024]

[0025] Where m and n are the components of the normal unit vector outside the integration loop;

[0026] σ xx is the normal stress in the x direction, σ yy is the normal stress in the y direction; τ xy is the shear stress acting on the xy plane, and σ xx , σ yy , τ xy is the stress component time history data obtained in step S2;

[0027] For plane stress problems, the strain energy density ω is expressed as:

[0028]

[0029] In the formula, ε xx is the positive strain in the x direction, ε yy is the positive strain in the y direction, γ xy is the shear strain acting on the xy plane; and ε xx , ε yy , γ xy is the strain component time history data obtained in step S2;

[0030] Substituting formula (2) and formula (3) into formula (1), we get

[0031]

[0032] The stress intensity factor at the crack tip is K I From the following formula:

[0033]

[0034] Where E is the elastic modulus.

[0035] In some embodiments, the stress intensity factor history obtained in step S3 is processed by a rain flow counting method to obtain a plurality of stress intensity factor cycles, and a stress intensity factor range and a corresponding number of cycles are calculated for each stress intensity factor cycle.

[0036] In some embodiments, in step S4, the stress intensity factor range and the corresponding number of cycles can be substituted into the Paris formula to calculate the crack extension length. The Paris formula is shown as follows:

[0037]

[0038] Where da is the crack extension length within a time period; dN is the number of loading cycles when the crack extension length is da; ΔK is the stress intensity factor range; C and m are the fatigue crack extension parameters of the hull structure material.

[0039] 1. Based on the above technical scheme, the present invention can simply and quickly calculate the local structural crack extension length through the range of stress intensity factors near the crack tip by the rain flow counting method, providing a solution for the crack extension prediction research of large components such as hull structures, and providing a reference for the structural safety of the hull. The method is easy to implement, has high calculation accuracy, high efficiency and high operability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0041] Figure 1 A flow chart of a method for calculating crack propagation length of a hull structure based on stress monitoring according to an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of stress monitoring area selection for a method for calculating crack propagation length of a hull structure based on stress monitoring according to an embodiment of the present invention;

[0043] Figure 3 A schematic diagram of path-independent integration of a method for calculating crack propagation length of a hull structure based on stress monitoring according to an embodiment of the present invention;

[0044] Figure 4 This is a diagram showing the arrangement of measuring points on a hull structure according to an embodiment of the present invention;

[0045] Figure 5 is a curve showing the stress response of the hull structure of the present embodiment changing with time;

[0046] Figure 6 It is a schematic diagram of a curve of stress response changing with time rotated 90° according to an embodiment of the present invention;

[0047] Figure 7 The stress time history curves of measuring points 1 to 4 in the embodiment of the present invention;

[0048] Figure 8 The strain history curves of measuring points 1 to 4 in the embodiment of the present invention;

[0049] Fig. 9 1 is a time history curve of stress intensity factor at measuring point 1 to measuring point 4 in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is described and illustrated below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments provided in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0051] Obviously, the drawings described below are only some examples or embodiments of the present application. For ordinary technicians in this field, the present application can also be applied to other similar scenarios based on these drawings without creative work. In addition, it can also be understood that although the efforts made in this development process may be complicated and lengthy, for ordinary technicians in this field related to the content disclosed in this application, some changes in design, manufacturing or production based on the technical content disclosed in this application are just conventional technical means, and should not be understood as insufficient content disclosed in this application.

[0052] Reference to "embodiments" in this application means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those of ordinary skill in the art that the embodiments described in this application may be combined with other embodiments without conflict.

[0053] A method for calculating the crack propagation length of a hull structure based on stress monitoring is described in this embodiment by taking a through crack as an example. Figure 1 As shown in the flowchart, the specific steps include:

[0054] S1. Determine the stress monitoring area during crack propagation;

[0055] In the local area where the through cracks occur in the hull structure, a stress monitoring area is set along the crack propagation direction. Specifically, a large rectangular area that can contain the crack tip is selected as the initial stress monitoring area D 0 , when the crack extends beyond the initial stress monitoring area D 0 When the range is within the range of , the initial stress monitoring area D is monitored according to the direction of crack propagation. 0 Extend and adjust to form a new rectangular stress monitoring area D 1 , when the crack extends beyond the stress monitoring area D 1 When the range is reached, continue to monitor the stress monitoring area D according to the direction of crack propagation. 1 Extend and adjust to form a new rectangular stress monitoring area D 2 , and so on, as the crack expands, new stress monitoring areas D are continuously formed. i (i=1, 2, 3, ...), so that in the process of the crack extending from the length to be monitored to the dangerous length, the crack is in the initial stress monitoring area D 0 Or stress monitoring area D i within the range.

[0056] S2, selecting a measuring point in the stress monitoring area, and obtaining a stress component time history and a strain component time history of the measuring point;

[0057] Specifically, first select the rectangular initial stress monitoring area D 0 The four vertex positions of are used as measuring points, and monitoring equipment is set on the measuring points. The monitoring equipment is used to measure the stress component time history and strain component time history around the crack tip during the crack extension process; in this embodiment, the initial stress monitoring area D 0 and stress monitoring area D i They are all square structures with a side length of 50 mm, that is to say, Figure 3As shown in the figure, the distance between two adjacent measuring points is 50 mm; Figure 4 The diagram shows the arrangement of measuring points on the hull structure of this embodiment, the position marked by the red dot is the measuring point position, and the yellow line is the crack extension direction. The monitoring equipment of this embodiment is a strain gauge, which measures the stress component time history and strain component time history around the crack tip during the crack extension process. At the same time, the strain gauge is connected to a data collector, which is used to collect and output the stress and strain data monitored by the strain gauge at the measuring point position when the hull is sailing.

[0058] As the crack expands, a new stress monitoring area D is formed. i When the measuring point is changed to the stress monitoring area D i The strain gauges are transferred to the stress monitoring area D at the four vertices of i on the measuring point.

[0059] like Figure 2 As shown in the figure, in order to prevent the crack from extending too fast and causing the strain gauge to be arranged in time, so that the data loss affects the subsequent crack extension length calculation, multiple stress monitoring areas D can be delineated in advance. i , and in these stress monitoring areas D i Lay out strain gauges in advance.

[0060] Since crack growth occurs over a period of time, the data logger collects stress and strain components over a period of time, including the normal stress σ in the x-direction. xx , normal stress in y direction σ yy , the shear stress τ acting on the xy plane xy , positive strain ε in the x direction xx , positive strain in the y direction ε yy , shear strain γ acting on the xy plane xy , output the above stress and strain data to a file through a data logger as input for subsequent calculation of stress intensity factor history;

[0061] S3, calculate the crack tip stress intensity factor time history;

[0062] The data collector of this embodiment outputs the monitoring data of stress and strain components within 1 minute each time, and the stress intensity factor time history within 1 minute can be calculated based on the time history data of stress and strain components; specifically, it includes:

[0063]

[0064] Where I is the path-independent integral, which represents the energy release rate at the crack tip;

[0065] Γ is a curve around the crack tip;

[0066] ω is the strain energy density; T x , T y is the component force acting on the unit length of the integrating loop;

[0067] u x ,u y is the displacement component; ds is the integral arc length;

[0068] Substituting it into formula (2) we get:

[0069] Among them, T x , T y The following conditions must be met:

[0070]

[0071] Where m and n are the components of the normal unit vector outside the integration loop;

[0072] σ xx is the normal stress in the x direction, σ yy is the normal stress in the y direction; τ xy is the shear stress acting on the xy plane, and σ xx , σ yy , τ xy is the stress component time history data obtained in step S2;

[0073] For plane stress problems, the strain energy density ω is expressed as:

[0074]

[0075] In the formula, ε xx is the positive strain in the x direction, ε yy is the positive strain in the y direction, γ xy is the shear strain acting on the xy plane; and ε xx , ε yy , γ xy is the strain component time history data obtained in step S2;

[0076] Substituting formula (2) and formula (3) into formula (1), we get

[0077]

[0078] The stress intensity factor at the crack tip is K I From the following formula:

[0079]

[0080] Where E is the elastic modulus.

[0081] In this embodiment, each rectangular stress monitoring area D iThe four sides of the crack tip are used as the independent integral paths for calculating the stress intensity factor at the crack tip. i The integral path is divided into 4 regions and 8 segments, and the integral path goes counterclockwise around the crack tip, such as Figure 3 As shown in the figure, the stress and strain components used in the calculation of the integral points on each integral path are approximately the stress monitoring area D directly connected to it. i The stress and strain components measured by the monitoring equipment at the vertex of the path, that is, the stress and strain components of the integration points on paths 1 and 2 are approximately the stress and strain components at the measuring point 1. Similarly, the stress and strain components of the integration points on the paths in the other three regions are approximately the stress and strain components at the three measuring points. The integral value I obtained for each path is added together to finally obtain the stress intensity factor at the crack tip.

[0082] The length of the integral path can be obtained by measuring the distance between the measuring points. The length of the integral path in this embodiment is 50 mm. Substituting the stress component, strain component, and integral path length into the formula, the stress intensity factor time history K at the crack tip can be calculated. I .

[0083] In this embodiment, the data collector outputs the stress and strain data recorded by the strain gauge once every 1 minute. According to the stress and strain component time history of the crack tip within 1 minute, the stress intensity factor time history of the crack tip can be calculated according to the above integral path by substituting into the formula. The stress, strain and stress intensity factor time history are shown in Error! Reference source not found. -Error! Reference source not found.;

[0084] The above calculated stress intensity factor history cannot be used directly to calculate the crack extension length. In this embodiment, the stress intensity factor history is processed by the rain flow counting method to obtain multiple stress intensity factor cycles, and the stress intensity factor range and the corresponding number of cycles can be calculated for each cycle.

[0085] Ships are affected by irregular wave loads at sea, and the hull structure will produce irregular stress responses under the action of irregular waves. The calculation of fatigue crack growth generally requires a regular stress response cycle. The rain flow counting method can convert irregular stress response time history curves into multiple regular stress response cycles for crack growth calculation.

[0086] The implementation method of the rain flow counting method is as follows:

[0087] With time as the horizontal axis and load as the vertical axis, Figure 5 As shown, a curve showing the stress response of the hull structure changing with time can be given, also known as a response-time history curve, which can be obtained through a stress monitoring device.

[0088] Rotate the response-time history curve 90 degrees, as shown in Figure 6 As shown; consider the response history as a multi-layer roof, and imagine that a raindrop starts to flow down along the maximum peak or valley. If there is no roof blocking it, the raindrop will reverse and continue to flow to the end point; if there is a lower roof blocking it, the raindrop will fall to the lower roof and then continue to flow down along the roof.

[0089] Record the maximum peak and valley values ​​of the raindrop flow, and take the path of the raindrop as a complete response cycle. Delete the part where the raindrop has flowed from the response-time history curve, and then repeat the above rain flow counting process for the remaining curves until there are no curves left. The main parameters of each response cycle, such as stress range and average stress, can be read from the graph.

[0090] Finally, the load cycles and load parameters obtained after rainflow counting, including stress range and average stress, are listed in a table for calculation. Rainflow counting uses dual-parameter counting. With the two parameters of stress range and average stress, the load cycle can be completely determined. Compared with other counting methods, the advantage of rainflow counting method is that the counting results are all full cycles, which can be directly used for crack growth calculation.

[0091] S4, based on the stress intensity factor history obtained in step S3, calculating the crack extension length by using the Paris formula;

[0092] The stress intensity factor range and the corresponding number of cycles can be substituted into the Paris formula to calculate the crack extension length. The Paris formula is shown as follows:

[0093]

[0094] In this implementation, since the number of cycles corresponding to each stress intensity factor range is 1, the Paris formula can be simplified to:

[0095] da=C(ΔK) m

[0096] Wherein: da is the crack extension length within 1 min; ΔK is the stress intensity factor range obtained by the rain flow counting method; C and m are fatigue crack extension parameters of the hull structure material, which are obtained in advance through crack extension tests. The range values ​​of some intensity factors calculated according to the stress intensity factor time history in this embodiment are shown in Table 1:

[0097] Table 1

[0098] Serial number Stress intensity factor range 1 0.347427 2 10.558 3 4.148 4 11.074 5 16.220 6 35.677 7 92.814 8 105.141 9 2.184 10 9.604 11 1.679 12 1.775

[0099] The crack extension length da within 1 minute can be calculated ij , the crack only starts from a small stress monitoring area Di Develop to the next small stress monitoring area D j When the crack propagation length is calculated based on the data of the four new stress monitoring points, the crack is in the previous small stress monitoring area D i The total extended length is da i , so the total extension length of the crack from the time when monitoring is required to the time when the crack reaches the dangerous length can be expressed as:

[0100] a=a 0 +(da 1 +da 2 +…+da n )

[0101] =a 0 +[(da 11 +da 12 +…+da 1n )+(da 21 +da 22 +…+da 2n )+…+(da n1 +da n2 +…+da nn )]

[0102] Substituting the above stress intensity factor range into the formula, the calculated crack extension length is shown in Table 2:

[0103] Table 2

[0104]

[0105] Based on the above embodiments, the technical solution can simply and quickly calculate the local structural crack extension length through the range of stress intensity factors near the crack tip by the rain flow counting method, provide a solution for the crack extension prediction research of large components such as hull structures, and provide a reference for the structural safety of the hull. The method is easy to implement, has high calculation accuracy, high efficiency and high operability.

[0106] Finally, it should be noted that: the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0107] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, a person skilled in the art should understand that the specific implementation mode of the present invention can still be modified or some technical features can be replaced by equivalents without departing from the spirit of the technical solution of the present invention, which should be included in the scope of the technical solution for protection of the present invention.

Claims

1. A method for calculating the crack propagation length of a hull structure based on stress monitoring, characterized in that: The steps include: S1. Determine the stress monitoring area during crack propagation; S2, selecting a measuring point in the stress monitoring area, and obtaining a stress component time history and a strain component time history of the measuring point; S3, calculate the crack tip stress intensity factor time history; S4. Based on the stress intensity factor history obtained in step S3, the crack extension length is calculated using the Paris formula.

2. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 1 is characterized in that: In step S1, a rectangular area that can contain the crack tip is selected as the initial stress monitoring area D0. When the crack extends beyond the range of the initial stress monitoring area D0, the initial stress monitoring area D0 is extended and adjusted according to the direction of the crack extension to form a new rectangular stress monitoring area D0. i (i=1, 2, 3...N), so that in the process of the crack extending from the length to be monitored to the dangerous length, the crack is in the initial stress monitoring area D0 or the stress monitoring area D i within the range.

3. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 2 is characterized in that: The four vertex positions of the initial stress monitoring area D0 are measuring points, and monitoring equipment is set on the measuring points, and the monitoring equipment is used to measure the stress component time history and strain component time history around the crack tip during the crack expansion process; As the crack expands, the stress monitoring area D is formed. i When , the position of the measuring point also changes to the stress monitoring area D i The monitoring device is transferred to the stress monitoring area D i on the measuring point.

4. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 3 is characterized in that: In order to prevent the crack from extending too fast and the monitoring equipment from being arranged in time, which may cause the loss of data and affect the subsequent calculation of the crack extension length, multiple stress monitoring areas D are defined in advance in step S2. i , and in the stress monitoring area D i The monitoring equipment is deployed at the measuring points.

5. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 4 is characterized in that: The monitoring device is connected to a data collector, and the data collector is used to collect the stress component time history data and the strain component time history data monitored by the monitoring device at the measuring point position.

6. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 1, characterized in that: The specific steps of calculating the crack tip stress intensity factor time history in step S3 include: Where I is the path-independent integral, which represents the energy release rate at the crack tip; Γ is a curve around the crack tip; ω is the strain energy density; T x , T y is the component force acting on the unit length of the integrating loop; u x ,u y is the displacement component; ds is the integral arc length; Among them, T x , T y The following conditions must be met: Where m and n are the components of the normal unit vector outside the integration loop; σ xx is the normal stress in the x direction, σ yy is the normal stress in the y direction; τ xy is the shear stress acting on the xy plane, and σ xx , σ yy , τ xy is the stress component time history data obtained in step S2; For plane stress problems, the strain energy density ω is expressed as: In the formula, ε xx is the positive strain in the x direction, ε yy is the positive strain in the y direction, γ xy is the shear strain acting on the xy plane; and ε xx , ε yy , γ xy is the strain component time history data obtained in step S2; Substituting formula (2) and formula (3) into formula (1), we get The stress intensity factor at the crack tip is K I From the following formula: Where E is the elastic modulus.

7. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 6, characterized in that: The stress intensity factor history obtained in step S3 is processed by a rain flow counting method to obtain a plurality of stress intensity factor cycles, and a stress intensity factor range and a corresponding number of cycles are calculated for each stress intensity factor cycle.

8. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 1, characterized in that: In step S4, the stress intensity factor range and the corresponding number of cycles can be substituted into the Paris formula to calculate the crack extension length. The Paris formula is shown as follows: Where da is the crack extension length within a time period; dN is the number of loading cycles when the crack extension length is da; ΔK is the stress intensity factor range; C and m are the fatigue crack extension parameters of the hull structure material.

9. The method for calculating the crack propagation length of a hull structure based on stress monitoring according to claim 1, characterized in that: The monitoring device is a strain gauge.

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