GB2614352A - Hydraulic bulge testing method and system for material properties of HDPE - Google Patents

Abstract

A hydraulic bulge testing method for material properties of high-density polyethene (HDPE), includes: testing material properties of a specimen through a uniaxial tensile test and hydraulic bulge test, and obtaining tensile experiment data and bulge experiment data; conducting finite element modelling according to the tensile experiment data and the bulge experiment data, and obtaining modelled tensile data and modelled bulge data; and comparing the modelled tensile data and the tensile experiment data, and obtaining a mechanical response relation of the specimen. The method enables providing a control of finite element for hydraulic expansion experiment to explain phenomenon of experiment process from an angle of numerical analysis, thus improving accuracy of the HDPE material mechanical property analysis.

Description

HYDRAULIC BULGE TESTING METHOD AND SYSTEM FOR MATERIAL

PROPERTIES OF HDPE

TECHNICAL FIELD

1011 The present disclosure relates to the technical field of bulge experiment testing, and in particular to a hydraulic bulge testing method and system for material properties of high-density polyethylene (HDPE).

BACKGROUND ART

1021 High-density polyethylene (HDPE) is widely used in transportation of drinking water, discharge of domestic water, underground transportation of municipal water, transportation of natural gas, telecommunications, some heating pipelines, transmission of solid and liquid media in medical systems and many other aspects.

1031 Compared with traditional metals, HDPE has many advantages, thereby becoming the optimal choice for a city pipe network. However, a current development and application level of HDPE pipes in China is generally low, which is still a certain degree lower than a foreign advanced level. How to correctly evaluate mechanical properties and damage behaviors of the HDPE pipes is the first problem to be faced, for making them widely used in China. The HDPE pipes are typical plastic pipes, with a main load form being internal pressure. Therefore, the research on bearing capacity of the HDPE pipes under the internal pressure is an important basis for correct understanding and use of the HDPE pipes, and is also one of the crucial means to evaluate raw materials of pipes.

1041 There are three main failure modes of the HDPE pipes under the internal pressure. The first is ductile damage. The HDPE pipes begin to creep and expand under high internal pressure. When creeping and expansion last for a certain time, weakest parts of the pipes suddenly bulge, and then are destroyed quickly. The second is brittle break. Under low internal pressure, tiny cracks in the pipes expand at crack tips under tearing stress, resulting in damage of the pipes. A speed of crack expansion is usually slow, which takes more than decades, so it is also called a slow cracking stage; and it is also possible that rapid crack expansion leads to instantaneous cracking, which is commonly referred to as rapid crack expansion. At present, accidents of the rapid crack expansion have been obviously prevented, so stress cracking generally refers to slow crack growth. The third is that deterioration of the whole materials of the HDPE pipes leads to brittle failure, which has been more than 50 years.

1051 For the HDPE pipes, both ductile failure and slow crack expansion are caused by yield in essence, but their yield mechanisms are different. There are two main yield mechanisms: shear yielding and a crazing phenomenon. The shear yielding is shear deformation of materials due to molecular slip during deformation. The ductile failure is a typical shear yielding process, where stress of the HDPE pipes under the internal pressure reaches or exceeds yield stress of the materials, resulting in damage of the HDPE pipes after the shear yielding. The slow crack expansion usually means that some impurities mixed in HDPE materials or defects or holes produced in a processing process cause stress concentration in the defects when the pipes are subjected to external forces, when the concentrated stress exceeds yield stress of HDPE, local crazing of the materials tends to occur, under the external forces, with increase of time, fibers in crazes tend to creep and fracture so as to produce cracks, then new crazes are further formed at new crack tips, and repeated occurrence of the process leads to crack continuous expansion. The expansion of cracks is accompanied by fracture of internal fiber structures of the cracks, and fracture of fibers in the crazes determines a crack expansion rate. Generally, it is considered that fibers break due to disentangling of molecular chains in or between the fibers, the service life of the HDPE pipes is predicted by means of the number of polymer linked molecules, and with the progress of the material synthesis technology, new pipes often have excellent resistance to slow crack expansion, with ductile damage areas increased gradually, so damage time can be as long as several decades. Therefore, the research on the ductile damage is also important.

1061 The mechanical properties of the HDPE pipes are usually analyzed through traditional tensile, bending, impact, hardness and hydraulic bulge experimental methods. A small punch experiment is an experimental method that uses a punch to punch a specimen sheet at a certain speed, records load-displacement (or deformation deflection) data of a specimen in the whole process from deformation to failure, and obtains various property parameters of the materials through analysis. However, due to concentrated loads on the specimen, it is difficult to create a relation between material properties and a force-displacement curve theoretically; evaluations of yield strength, tensile strength, fracture toughness, etc. are mostly empirical correlations, and different researchers have different empirical correlation formulas; and the empirical correlation formulas are greatly influenced by factors such as steel ball sizes, steel ball stiffness, steel ball centering and friction coefficients between steel balls and specimens. Compared with the small punch technology, the hydraulic bulge technology has the advantages that the specimen is subjected to uniformly distributed loads, which facilitates theoretical analysis and is not influenced by factors such as eccentricity and friction. A hydraulic bulge experiment has higher accuracy and cannot be limited by too many experimental conditions. However, the research on finite element modeling of an experimental process is obviously insufficient, and phenomena in the experimental process, such as local thinning and ductile damage, cannot be explained from an angle of numerical analysis.

SUMMARY

1071 An objective of the present disclosure is to provide a hydraulic bulge testing method and system for material properties of high-density polyethylene (HDPE), so as to solve the problems that the research on finite element modeling of an existing hydraulic bulge experimental process is insufficient, and phenomena in an experimental process cannot be explained from an angle of numerical analysis.

[081 To achieve the objective, the present disclosure provides a hydraulic bulge testing method for material properties of HDPE. The method includes: 1091 testing material properties of a specimen through a uniaxial tensile test and a hydraulic bulge test, and obtaining tensile experiment data and bulge experiment data; [101 conducting finite element modeling according to the tensile experiment data and the bulge experiment data, and obtaining modeled tensile data and modeled bulge data; and [11] comparing the modeled tensile data and the tensile experiment data, comparing the modeled bulge data and the bulge experiment data, and obtaining a mechanical response relation of the specimen.

[12] Optionally, the testing material properties of a specimen through a uniaxial tensile test, and obtaining tensile experiment data specifically includes: 1131 determining an engineering stress-strain curve according to characteristics of the specimen; [14] conducting uniaxial tension on the specimen, and recording real stress and strain, where 1151 assuming that a size does not change during tension, the real stress and strain satisfies a formula: [16] 2 = ln(1+ c) [17] = o-(1+ c) [18] where 6 is engineering strain, si is real strain, and a and a indicate engineering stress and real stress respectively; and [19] selecting a Poisson's ratio, adding the Poisson's ratio into a real stress and strain satisfying formula, and obtaining a real stress and strain curve.

[20] Optionally, before the testing material properties of a specimen through a uniaxial tensile test, and obtaining tensile experiment data, the method specifically includes: [21] determining a superelastic model of the specimen to be a Marlow constitutive model for representing nonlinear elasticity of the specimen, [22] determining a plastic model of the specimen through isotropic power law = 0 hardening; and [23] selecting a ductile criterion to determine a damage evolution law.

[24] Optionally, the conducting finite element modeling according to the tensile experiment data, and obtaining modeled tensile data specifically includes.

[25] creating a tensile finite element model for a specimen subjected to uniaxial tension; [26] conducting grid division on the tensile finite element model by using a three-dimensional eight-node reduced integration element; and [27] using an explicit scheme integral ABAQUS/Explicit, setting a density and a total mass scaling value, controlling loading displacement and a loading rate to be consistent with those in the uniaxial tensile test, conducting a modeling experiment, and obtaining the modeled tensile data, where the modeled tensile data includes a load-displacement curve, equivalent strain cloud diagrams for different loading displacement, a failure mechanism, a failure position and a port shape.

[281 Optionally, the testing material properties of a specimen through a hydraulic bulge test, and obtaining bulge experiment data specifically includes: 1291 using a hydraulic bulge experiment device to conduct a bulge test on the specimen, and obtaining bulge displacement data and specimen strain and stress data.

[30] Optionally, the conducting finite element modeling according to the bulge experiment data, and obtaining modeled bulge data specifically includes: [31] creating a hydraulic bulge finite element model according to a hydraulic bulge experiment device; 1321 conducting grid division on the hydraulic bulge finite element model by using a three-dimensional eight-node reduced integration element; [33] setting a hourglass control stiffness parameter in a first-order reduced integration element, so as to obtain a refined grid; [341 using an explicit scheme integral ABAQUS/Explicit, setting a total mass scaling value, setting a fixture as metal, setting an elastic modulus, a Poisson's ratio and a density, and conducting description by using an isotropic linear elastic constitutive model; and [35] setting a bottom end of the fixture as a fixed end, constraining all freedom degrees, and meanwhile applying symmetry constraints in X and Y directions to two symmetry planes respectively; setting friction contact on upper and lower surfaces of the specimen, and setting a friction coefficient; and using a pressure loading mode, applying pressure to the lower surface of the specimen at a constant speed according to experimental pressure, and obtaining the modeled bulge data, where the modeled bulge data includes a deformation and strain cloud diagram, a pressure-displacement curve, a damage distribution cloud diagram and local thinning data.

[36] Optionally, the comparing the modeled tensile data and the tensile experiment data, and obtaining a mechanical response relation of the specimen specifically includes: [37] analyzing a tension deformation law of the specimen according to a load-displacement curve and equivalent strain cloud diagrams for different loading displacement; [38] determining a necking change of the specimen according to a failure mechanism and a failure position; and 1391 determining an evolution law of the specimen from tension to fracture according to the necking change and a port shape.

[40] Optionally, the comparing the modeled bulge data and the bulge experiment data, and obtaining a mechanical response relation of the specimen specifically includes: [41] analyzing a specimen bulge deformation law according to the deformation and strain cloud diagram and the pressure-displacement curve obtained through modeling and an experiment; [42] predicting a fracture position of the specimen according to the damage distribution cloud diagram; and [43] analyzing a specimen thinning law according to the local thinning data [44] A hydraulic bulge testing system for material properties of HDPE includes: [45] an experiment element configured to test material properties of a specimen through a uniaxial tensile test and a hydraulic bulge test, and obtain tensile experiment data and bulge experiment data; 1461 a modeling element configured to conduct finite element modeling according to the tensile experiment data and the bulge experiment data, and obtain modeled tensile data and modeled bulge data; and [47] an analysis element configured to compare the modeled tensile data and the tensile experiment data, compare the modeled bulge data and the bulge experiment data, and obtain a mechanical response relation of the specimen.

[48] Optionally, the modeling element includes a tensile modeling module and a bulge modeling module; [49] the tensile modeling module is configured to: [50] create a tensile finite element model for a specimen subjected to uniaxial tension; 1511 conduct grid division on the tensile finite element model by using a three-dimensional eight-node reduced integration element; and 1521 use an explicit scheme integral ABAQUS/Explicit, set a density and a total mass scaling value, control loading displacement and a loading rate to be consistent with those in the uniaxial tensile test, conduct a modeling experiment, and obtain the modeled tensile data, where the modeled tensile data includes a load-displacement curve, equivalent strain cloud diagrams for different loading displacement, a failure mechanism, a failure position and a port shape; and 1531 the bulge modeling module is configured to: [54] create a hydraulic bulge finite element model according to a hydraulic bulge experiment device, 1551 conduct grid division on the hydraulic bulge finite element model by using a three-dimensional eight-node reduced integration element; 1561 set a hourglass control stiffness parameter in a first-order reduced integration element, so as to obtain a refined grid; [57] use an explicit scheme integral ABAQUS/Explicit, setting a total mass scaling value, setting a fixture as metal, setting an elastic modulus, a Poisson's ratio and a density, and conducting description by using an isotropic linear elastic constitutive model; and 1581 set a bottom end of the fixture as a fixed end, constrain all freedom degrees, and meanwhile apply symmetry constraints in X and Y directions to two symmetry planes respectively; set friction contact on upper and lower surfaces of the specimen, and set a friction coefficient; and use a pressure loading mode, apply pressure to the lower surface of the specimen at a constant speed according to experimental pressure, and obtain the modeled bulge data, where the modeled bulge data includes a deformation and strain cloud diagram, a pressure-displacement curve, a damage distribution cloud diagram and local thinning data.

[59] According to specific examples provided in the present disclosure, the present disclosure has the following technical effects: [60] Compared with an existing model, the hydraulic bulge testing method and system for material properties of HDPE provided in the present disclosure reflect different mechanical properties, have fewer uncertain parameters, and more intuitively reflect related mechanical properties of the HDEP. In addition, the present disclosure analyzes nonlinear elasticity of the HDPE, improves accuracy of mechanical property analysis, and solves an inaccuracy problem due to the fact that the existing model mostly analyzes linear elasticity.

[61] The present disclosure also effectively analyzes and describes ductile damage of the HDEP, and provides a technical basis for damage prediction of the HDEP.

1621 The present disclosure provides a contrast of a finite element method for a hydraulic bulge experiment, such that the hydraulic bulge experiment may also explain a phenomenon in an experimental process from an angle of numerical analysis, such as local thinning and ductile damage, thereby further improving accuracy of mechanical property analysis of the HDPE.

BRIEF DESCRIPTION OF THE DRAWINGS

[63] To more clearly illustrate technical solutions in the examples of the present disclosure or in the prior art, a brief introduction to the accompanying drawings required for the examples will be provided below. Obviously, the accompanying drawings in the following description are only some of the examples of the present disclosure, and those of ordinary skill in the art would also be able to derive other drawings from these drawings without making creative efforts.

[64] FIG. 1 is a schematic diagram of a size of an axial tensile specimen; 1651 FIG. 2 is an engineering stress and strain relation curve graph of high-density polyethylene (HDPE); [66] FIG. 3 is a real stress and strain curve graph of the HDPE; [67] FIG. 4 is a schematic diagram of strain decomposition; [68] FIG. 5 is a tensile finite element model of a uniaxial tensile specimen; [69] FIG. 6 is a comparison diagram of experimental and modeled load-displacement curves; [70] FIG. 7 is an equivalent strain cloud diagram when loading displacement is 31 mm in modeling; [71] FIG. 8 is a schematic diagram of a uniaxial tensile damage evolution process; [72] FIG. 9 is a comparison diagram of fractures after tension, where a is a finite element fracture and b is an experimental fracture; [73] FIG. 1 0 is a flow diagram of a hydraulic bulge experiment device; [74] FIG. 11 is a bulge finite element model of a hydraulic bulge experiment; [75] FIG. 12 is a strain cloud diagram with pressure of 8 Mpa; [76] FIG. 13 is a comparison diagram of experimental and modeled pressure-displacement curves, where a is a finite element modeling diagram and b is an experimental result diagram; [77] FIG. 14 is a damage distribution cloud diagram of a bulging specimen before fracture; [78] FIG. 15 is a schematic diagram of local thinning; and [79] FIG. 16 is a graph showing change of a thinning thickness with loads.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[801 The technical solution in the examples of the present disclosure is clearly and completely described below with reference to the accompanying drawings in the examples of the present disclosure. Apparently, the described examples are merely some rather than all of the examples of the present disclosure. All the other examples obtained by those of ordinary skill in the art based on the examples in the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.

1811 Objectives of the present disclosure are to conduct a uniaxial tensile experiment and a hydraulic bulge experiment on high-density polyethylene (HDPE) and to conduct finite element modeling and numerical modeling on an experimental process. A description method of an HDPE constitutive relation and a failure mode was rationally selected, mechanical response of a specimen in the experimental process was analyzed, and physical characteristics such as local thinning were discussed, so as to deeply understand the failure mode of the HDPE.

[82] To make the objectives, features, and advantages of the present disclosure more apparent and easily understood, the present disclosure will be described in detail below with reference to the drawings and specific implementations.

1831 A hydraulic bulge testing method for material properties of HDPE provided in the example included: 1841 material properties of a specimen were tested through a uniaxial tensile test and a hydraulic bulge test, and tensile experiment data and bulge experiment data were obtained; 1851 finite element modeling was conducted according to the tensile experiment data and the bulge experiment data, and modeled tensile data and modeled bulge data were obtained; and [86] the modeled tensile data and the tensile experiment data were compared, the modeled bulge data and the bulge experiment data were compared, and a mechanical response relation of the specimen was obtained.

[87] Each step was described in detail in conjunction with examples below.

1881 I, Material properties of a specimen were tested through a uniaxial tensile test, and tensile experiment data was obtained 1891 1.1 Specimens and experiment apparatus [90] The specimens involved in the example were all PESO M7600 raw materials produced by Sinopec Yanshan Petrochemical Company, and flaky specimens were all prepared by a single screw injection molding process, where an injection temperature was 165°C. A size of a uniaxial tensile specimen was as shown in FIG. I. [91] ASTMD638-10 having a wider allowable specimen thickness range was selected as a reference standard for a mechanical tensile experiment of the HDPE.

[92] In a tensile experiment, a 0WT4503 universal testing machine provided by SANS was used, and a DBX-800 large deformation extensometer was used to ensure experiment accuracy. An experiment reference standard was ASTMD638, and an experiment temperature was controlled to be 25±3°C during tension. There were 3 parallel specimens. In an experiment, displacement loading was used and a loading rate was controlled to be 2 mm/min.

1931 1.2 Engineering stress and strain relation [94] In the example, the used engineering stress and strain relation of the HDPE was closer to mechanical response of metal, as shown in FIG. 2. During uniaxial tension, a stress and strain curve included: [95] AB-section elastic deformation: stress in an area before a yield point increased with increase of strain, and change of the stress and strain curve deviated from a straight-line trend. A remarkable feature of the area was that deformation may slowly recover as external force was removed.

1961 BC-section elastic-plastic deformation: yield occurred at B to reach a maximum value of the engineering stress and strain curve, resulting in plastic deformation, strain softening of a BC section led to a necking phenomenon, stress decreased with increase of strain, and in the process, a polymer interior underwent very complicated changes: from a spherulitic crystal structure to a fiber structure, and finally to molecular chain pulling off and fracture.

[97] It may be seen from FIG. 2 that a stress and strain curve of polyethylene may be approximately considered as a linear relation only within a small range, and overall performance was a nonlinear relation. At an initial stage of deformation, stress increased with increase of deformation. Meanwhile, a nonlinear relation between stress and strain was more obvious. After yielding, a material softened and fell until finally breaking.

1981 1.3 Real stress and strain relation [99] An engineering stress and strain curve was based on an assumption that a cross-sectional area and a specimen length did not change during tension. During actual tension, a cross section of a tensile specimen was continuously slightly reduced, and strain of the HDPE was larger than those of common metals, so a real stress and strain situation should be considered.

[100] Assuming that a size did not change during tension, the real stress and strain satisfied: [101] sr =1n(1+6) [102] CT (1+ 8) [103] where & was engineering strain, ST was real strain a and '72-indicated engineering stress and real stress respectively.

[104] A size of an HDPE specimen varied during actual tensile deformation, so a Poisson's ratio should be considered. For a polymer material, a Poisson's ratio was usually 0.38. FIG. 3 shows a real stress and strain curve of the HDPE.

[105] II, HDPE constitutive model [106] 2.1 Superelastic model [107] A material constitutive model used a mathematical function to describe stress response of a material under given strain. A Marlow method may accurately describe an elastic behavior of the material until strain reached 0.6, so a Marlow constitutive model was selected to represent nonlinear elasticity of the HDPE in the example.

[108] In addition to a feature of nonlinear elasticity, after strain reached 0.2, local plastic deformation made a tensile specimen have an obvious necking phenomenon, which led to decrease of a bearing area and stress. The mechanism caused an error between the Marlow constitutive model and an experimental curve at a later stage of loading, which indicates that influence of plasticity cannot be ignored.

[109] 2.2 Plastic model [110] In experiment data provided strain included plastic strain and total strain of the material. Therefore, the total strain had to be decomposed into elastic and plastic strain components.

[111] c [112] EP was real plastic strain, 6 was overall real strain, and was real elastic strain. For a linear elastic material, elastic strain was equal to a ratio of real stress to a Young's modulus. In the example, a Marlow constitutive model was selected to describe a nonlinear elastic behavior, at an early stage of deformation, an elastic modulus changed greatly, while an elastic modulus of the material after yielding may be regarded as basically unchanged, which indicated linear elasticity. Therefore, the plastic strain may be computed by the following formula: [113] 611 = c -c "= c -c -Ac IF [114] ' was total strain before yielding, E was a tangent modulus of a yield point, and acr = -5. was a difference between real stress and yield stress. A schematic diagram was as shown in FIG. 4.

-

rf = k (r:0-Fr;) [115] In the example, isotropic power law hardening was used to describe a plastic strain curve, which was a plastic model Parameters were listed in Table 1.

[116] Table 1 Plastic model fitting parameters k go 39,85 0,135 0.117 [117] 2.3 Ductile damage model [118] In the example, a ductile criterion was selected to determine the start of damage, which was used to predict damage caused by development of holes. A model assumed that equivalent plastic strain at the beginning of damage was a function of stress triaxiality and a strain rate: [119] [120] 11=-p I q was stress triaxiality, was pressure stress, q was Nfises equivalent stress, and was an equivalent plastic strain rate When the following conditions were satisfied, a damage initial criterion was achieved: ds [121] WD = =1 (77,e1)1 [122] IV') was a state variable that monotonically increases with plastic deformation.

Once a set initial criterion was satisfied, stiffness of a material may deteriorate according to a damage evolution law specified in the criterion.

[123] The damage evolution law described a deterioration rate of the stiffness of the material, and ABAQUS assumed that stiffness deterioration related to an active failure mechanism may be modeled by using a scalar damage variable D At any given time during analysis, a stress tensor in the material was given by a scalar damage equation: [124] [125] a was an effective (or undamaged) stress tensor computed in a current increment. a referred to stress existing in the material without damage. When D =1, the material lost bearing capacity. By default, if all nodes of any element lost bearing capacity, the element may be deleted from a model. In the example, an energy criterion provided by ABAQUS was used to define damage evolution, and energy (fracture energy) required for failure after start of damage was given to simulate fracture.

[126] III, Finite element modeling was conducted according to tensile experiment data, and modeled tensile data was obtained [127] 3.1 Tensile finite element model [128] A finite element model of a uniaxial tensile specimen was as shown in FIG. 5. In an actual experiment, a distance between clamps was 92.46 mm. In order to keep a loading condition consistent with an experiment, the tensile finite element model intercepted a specimen. The model included all parallel sections and a small part of transitional circular arc area.

[129] Considering that a specimen in modeling of a subsequent bulge experiment was subjected to a bending load, in order to avoid a possible shear self-locking phenomenon and to keep consistency between two examples, the example used a three-dimensional eight-node reduced integration element (C3D8R) to conduct grid division on the model. Because there was only one integration point in a center of a linear reduced integration element, which was equivalent to a constant stress element, a result on the integration point was relatively accurate, but node stress obtained through interpolation and averaging was not accurate enough. In the example, stress concentration of a single node was not involved, so element selection was considered to be feasible.

[130] 3.2 Load and boundary conditions [131] In the example, an explicit scheme integral ABAQUS/Explicit was used, a density was set as 0.9 Kg/mm3, and a total mass scaling value was 10. A loading mode of controlling displacement was used, and a loading rate was 2.00 mm/min, which was consistent with that in an experiment. A left end of a specimen was a fixed end, which constrained all freedom degrees, a clamping state was modeled, and loads were applied to a right end face.

[132] 3.3 Modeling result and experiment result analysis [133] 3.3.1 Deformation analysis [134] FIG. 6 shows load and displacement curves of the uniaxial tensile experiment and the finite element modeling of an HDPE specimen. It may be seen that a fracture process of the HDPE was divided into three parts: a large elastic deformation area, an elastic-plastic deformation area and a failure area. A selected mechanical model may accurately describe mechanical behaviors of materials in an elastic area and an initial plastic area, but damage developed rapidly in a later stage, resulting in fracture earlier than that in an experiment. Modeled fracture displacement was 3115 mm, while an experimental value was 33.78 mm, with an error of 7.78%.

[135] FIG. 7 shows an equivalent strain cloud diagram when loading displacement is 31 mm in modeling. It may be seen that a specimen was nearly uniformly deformed in an early stage of tension, and with increase of the loading displacement, deformation gradually concentrated in a small area on a right side, which was also an initial position of aging.

[136] 3.3.2 Necking analysis [1371 Due to existence of interfacial adhesion, initiation of cracks required considerable fracture energy and occurred under high stress, which may be seen from a damage evolution process of an increasing yield fracture process. Once a hole was formed, growth of the hole depended on stability of precursor elongation and resistance of a particle-matrix interface. A ductile damage criterion used herein was based on generation, growth and aggregation of holes in a material, which may well describe the above damage process as shown in FIG. 8.

[138] FIG. 8 shows that damage of a tensile specimen first occurs in a central position, and when damage of a central element reaches a critical value 1, damage of an adjacent element is only 0.16. A displacement load of the center element at the start of failure was smaller than those of other positions. On the whole, when tensile displacement was 15 mm, ductile damage of the HDPE reached an initial criterion, which was I" = l in formula 12. Then, a stage of damage evolution was entered, and finally fracture occurred when loading displacement was 30 mm. During the period, a damage quantity D developed exponentially, which was a result of rapid accumulation of fracture energy in a later period.

[139] 3.3.3 Fracture shape comparison [140] FIG. 9 shows a fracture shape comparison of a finite element modeling result (a) and an experimental result (b). The experimental result showed an obvious polymer fracture feature, that is, a long-chain deformation process was experienced, then crazing occurred, and microfiber fracture occurred at a fracture. In a finite element, a fracture fiber corresponded to significant deformation of an element at a later stage of loading.

As accumulated damage of individual elements reached a critical value when a necking position fails locally, a preset element deletion mechanism was triggered, deletion of some elements released stress at the fracture, and remaining elements were rapidly stretched, showing shape features of FIG. 9(a).

[141] IV, Material properties of a specimen were tested through a hydraulic bulge test, and bulge experiment data was obtained [142] 4.1 Hydraulic bulge experiment device [143] A self-made hydraulic bulge device was used, and the specimen was a disc specimen with a diameter of 10 mm, and a pressing rate was 0.2 MPa/min. As shown in FIG. 10, the hydraulic bulge devices mainly included a high-pressure pump, a pressure gage, a pressure sensor, a displacement sensor, a displacement transmission device, a data acquisition card, a computer, etc., and an experimental procedure was as shown in FIG. 10. An oil circuit was equipped with the pressure gage and the pressure sensor, where the pressure gage was mainly configured to facilitate observation of implementation of pressure by the experimental personnel, and a pressure signal was transmitted from the pressure sensor to the computer via the data acquisition card. Displacement produced by deformation of a center point of the specimen is transmitted to the displacement sensor via the displacement transmission device and then via the data acquisition card.

[144] V, Finite element modeling was conducted according to bulge experiment data, and modeled bulge data was obtained [145] 5.1 Bulge finite element model 11461 A finite element model of the hydraulic bulge experiment was as shown in FIG. 11, and a thickness of a specimen was 1 mm, which was consistent with that in an experiment. A bulge experiment model was an obvious axisymmetric model. Considering a computation speed and result accuracy of numerical modeling at the same time, a whole specimen was segmented in the study, and a 1/4 model was used for computation.

[147] Considering that the specimen in loading was subjected to a bending load, a three-dimensional eight-node reduced integration element (C3D8R) was used to conduct grid division on the model so as to avoid a shear self-locking phenomenon. In ABAQUS, a concept of 'hourglass stiffness' was introduced into a first-order reduced integration element, and computation accuracy of a reduced integration element may be effectively improved by rationally refining a grid. It was suggested that there were at least four layers of elements in a thickness direction, so for the example, the thickness direction of the specimen was divided into five layers so as to control computation errors.

[148] 5.2 Load and boundary conditions [149] Similarly, an explicit scheme integral ABAQUS/Explicit was used, and a total mass scaling value was 10. A fixture was made of metal, with an elastic modulus of 200 Gpa, a Poisson's ratio of 0.3 and a density of 7.9 Kg/mm3. Stiffness of the fixture was far greater than that of rubber, so an isotropic linear elastic constitutive model was used for description.

[150] Loading was consistent with that in an experiment, a pressure loading mode was used, and pressure was applied to a lower surface of a specimen at a constant speed of 0.2 Mpa/min. Considering control of freedom degrees, a bottom end of the fixture was set as a fixed end, which constrained all freedom degrees, and meanwhile applied symmetry constraints in X and Y directions to two symmetry planes respectively.

[151] Friction between the specimen and the fixture was also an important influence factor. In an actual experiment, a pressing ring had a downward pressure load, so it may be considered that there was large static friction between an HDPE sheet and the fixture. In modeling, friction contact was set on upper and lower surfaces of the specimen respectively, and a friction coefficient was set as 0.5.

[152] 5.3 Modeling result and experiment result analysis [153] 5.3.1 Deformation analysis [154] As shown in FIG. 12, it was obvious that there were two main deformation areas, where on area is at a bottom end of a specimen, the position is subjected to a tensile force, and plastic flow gradually occurred; and the other position was a top end of the specimen.

1155] FIG. 13 shows a pressure-displacement curve of an HDPE specimen obtained through the finite element modeling and a corresponding experimental result. There was a large preload (4 NIPa-6 NIPa) in an experiment, so an early result cannot be analyzed. However, it may be seen that change trends of pressure and displacement before failure of the specimen were completely consistent, including a change rate IdU of the pressure with the displacement, and both the pressure and displacement experienced a process of rising-falling-rising-falling.

11561 5.3.2 Damage analysis [157] FIG. 14 shows a damage distribution cloud diagram of a bulging specimen before fracture, where a position with a maximum damage value is an apex of the specimen, and damage extends in a ring shape. Compared with the other positions, a large deformation area is observed at the apex in an experiment. In addition, a contact position of a blank holder also had some damage development, which required attention, so as to prevent non-tip fracture in the experiment.

[158] The above results showed that a ductile damage method may also accurately predict a fracture position of the specimen in modeling of a bulge experiment. However, considering mechanical complexity of the HDPE, small changes of a loading rate, a temperature and other factors possibly led to a change of a damage behavior. Therefore, a lot of work needs to be done to determine model parameters in an early stage.

[159] 5.3.3 Local thinning analysis [160] In addition, in an experiment, it was observed that a top end of an HDPE specimen had an obvious local thinning phenomenon, which showed that a top thickness Hi was smaller than a side thickness H2, as shown in FIG. 15. The phenomenon was effectively represented in the finite element modeling. If HI and H2 were defined as thicknesses of the specimen at positions of 0 mm and 2 mm from a center point under no load, and DH -H2 -H1 was defined as a thinned thickness, such that a change law of the thinned thickness with loads shown in FIG. 16 may be obtained according to a finite element modeling result. The results showed that there was an obvious nonlinear relation between MT and applied pressure, and an HDPE sheet was at an elastic deformation stage in an early stage of loading. In this case, less thinning indicated that the specimen nearly uniformly bulged. By contrast, after pressure reached 2 MPa, the thinned thickness showed an obvious increase trend, which was a result of plastic flow of a material during loading. In addition, a third-order polynomial may be used to fit a relation between pressure and the thinned thickness.

[161] VI, Conclusion

[162] In the example, a constitutive model of the HDPE was revised through the uniaxial tensile test, various superelastic mechanical models and damage models were considered, and a tensile test and the hydraulic bulge experiment were subjected to finite element modeling and analysis. Obtained conclusions were as follows: [163] A superelastic constitutive relation may effectively describe a nonlinear elastic behavior of the HDPE, and an Marlow constitutive model showed better fitting accuracy. In ABAQUS that was commercial software, numerical modeling of an elastic stage of the HDPE may be realized by revising parameters.

[164] At a loading rate of 2 mm/min, the HDPE showed an obvious elastic-plastic mechanical behavior, including physical phenomena such as necking. Therefore, considering mechanical description of the HDPE, contribution of plastic deformation had to be considered, and a pure elastic constitutive model cannot be simply used.

[165] Fracture of the HDPE was caused by a ductile failure mechanism, which was an hole action formed by separation of crystal block boundaries and tensile extension of polymer chains at a microscopic level. The process may be represented by a ductile criteria failure model.

11661 An element type was selected rationally, and the above constitutive relations were combined, such that a uniaxial tensile process may be numerically reduced accurately. In the study, damage development and a necking phenomenon of modeling results were discussed, and fracture shapes obtained through modeling and an experiment were basically consistent.

[167] The finite element modeling of the hydraulic bulge experiment accurately predicted a deformation process and a failure position of a specimen.

11681 There was an obvious local thinning phenomenon in modeling of a bulge experiment, a thinning speed was low in an early stage of loading, and a thinned thickness increased obviously after applied pressure reached 2 MPa. The relation may be described by a third-order polynomial.

[169] The present disclosure further provides a system corresponding to the method. The hydraulic bulge testing system for material properties of HDPE includes: [170] an experiment element configured to test material properties of a specimen through a uniaxial tensile test and a hydraulic bulge test, and obtain tensile experiment data and bulge experiment data; [171] a modeling element configured to conduct finite element modeling according to the tensile experiment data and the bulge experiment data, and obtain modeled tensile data and modeled bulge data; and [172] an analysis element configured to compare the modeled tensile data and the tensile experiment data, compare the modeled bulge data and the bulge experiment data, and obtain a mechanical response relation of the specimen.

[1731 The modeling element includes a tensile modeling module and a bulge modeling module; [1741 the tensile modeling module is configured to: [175] create a tensile finite element model for a specimen subjected to uniaxial tension; [176] conduct grid division on the tensile finite element model by using a three-dimensional eight-node reduced integration element; and 11771 use an explicit scheme integral ABAQUS/Explicit, set a density and a total mass scaling value, control loading displacement and a loading rate to be consistent with those in the uniaxial tensile test, conduct a modeling experiment, and obtain the modeled tensile data, where the modeled tensile data includes a load-displacement curve, equivalent strain cloud diagrams for different loading displacement, a failure mechanism, a failure position and a port shape; and [178] the bulge modeling module is configured to: [179] create a hydraulic bulge finite element model according to a hydraulic bulge experiment device; [180] conduct grid division on the hydraulic bulge finite element model by using a three-dimensional eight-node reduced integration element, 11811 set a hourglass control stiffness parameter in a first-order reduced integration element, so as to obtain a refined grid, 11821 use an explicit scheme integral ABAQUS/Explicit, setting a total mass scaling value, setting a fixture as metal, setting an elastic modulus, a Poisson's ratio arid a density, and conducting description by using an isotropic linear elastic constitutive model; and 11831 set a bottom end of the fixture as a fixed end, constrain all freedom degrees, and meanwhile apply symmetry constraints in X and Y directions to two symmetry planes respectively; set friction contact on upper and lower surfaces of the specimen, and set a friction coefficient, and use a pressure loading mode, apply pressure to the lower surface of the specimen at a constant speed according to experimental pressure, and obtain the modeled bulge data, where the modeled bulge data includes a deformation and strain cloud diagram, a pressure-displacement curve, a damage distribution cloud diagram and local thinning data [184] Since the system disclosed in the examples corresponds to the method disclosed in the examples, the description is simple, and reference may be made to the method description 11851 In the description, several specific examples are used for illustration of the principles and implementations of the present disclosure. The description of the foregoing examples is used to help illustrate the method of the present disclosure and the core ideas thereof In addition, those of ordinary skill in the art may make various modifications in terms of specific implementations and the scope of application in accordance with the ideas of the present disclosure. In conclusion, the content of the description shall not be construed as a limitation to the present disclosure.

Claims (10)

1. WHAT IS CLAIMED IS: 1. A hydraulic bulge testing method for material properties of high-density polyethylene (HDPE), comprising: testing material properties of a specimen through a uniaxial tensile test and a hydraulic bulge test, and obtaining tensile experiment data and bulge experiment data; conducting finite element modeling according to the tensile experiment data and the bulge experiment data, and obtaining modeled tensile data and modeled bulge data; and comparing the modeled tensile data and the tensile experiment data, comparing the modeled bulge data and the bulge experiment data, and obtaining a mechanical response relation of the specimen.
2. 2. The hydraulic bulge testing method for material properties of HDPE according to claim 1, wherein the testing material properties of a specimen through a uniaxial tensile test, and obtaining tensile experiment data specifically comprises: determining an engineering stress-strain curve according to characteristics of the specimen; conducting uniaxial tension on the specimen, and recording real stress and strain, wherein assuming that a size does not change during tension, the real stress and strain satisfies a formula: = ln(1+ E) =o-(1+ e) wherein 6 is engineering strain, CT is real strain, and a and CT indicate engineering stress and real stress respectively; and selecting a Poisson's ratio, adding the Poisson's ratio into a real stress and strain satisfying formula, and obtaining a real stress and strain curve.
3. 3. The hydraulic bulge testing method for material properties of HDPE according to claim 1, wherein before the testing material properties of a specimen through a uniaxial tensile test, and obtaining tensile experiment data, the method further comprises: determining a superelastic model of the specimen to be a Marlow constitutive model for representing nonlinear elasticity of the specimen; determining a plastic model of the specimen through isotropic power law hardening = 1((r:0-Fr; ; and selecting a ductile criterion to determine a damage evolution law.
4. 4. The hydraulic bulge testing method for material properties of HDPE according to claim 1, wherein the conducting finite element modeling according to the tensile experiment data, and obtaining modeled tensile data specifically comprises: creating a tensile finite element model for a specimen subjected to uniaxial tension, conducting grid division on the tensile finite element model by using a three-dimensional eight-node reduced integration element; and using an explicit scheme integral ABAQUS/Explicit, setting a density and a total mass scaling value, controlling loading displacement and a loading rate to be consistent with those in the uniaxial tensile test, conducting a modeling experiment, and obtaining the modeled tensile data, wherein the modeled tensile data comprises a load-displacement curve, equivalent strain cloud diagrams for different loading displacement, a failure mechanism, a failure position and a port shape
5. 5. The hydraulic bulge testing method for material properties of HDPE according to claim 1, wherein the testing material properties of a specimen through a hydraulic bulge test, and obtaining bulge experiment data specifically comprises: using a hydraulic bulge experiment device to conduct a bulge test on the specimen, and obtaining bulge displacement data and specimen strain and stress data.
6. 6. The hydraulic bulge testing method for material properties of HDPE according to claim 1, wherein the conducting finite element modeling according to the bulge experiment data, and obtaining modeled bulge data specifically comprises: creating a hydraulic bulge finite element model according to a hydraulic bulge experiment device; conducting grid division on the hydraulic bulge finite element model by using a three-dimensional eight-node reduced integration element, setting a hourglass control stiffness parameter in a first-order reduced integration element, so as to obtain a refined grid, using an explicit scheme integral ABAQUS/Explicit, setting a total mass scaling value, setting a fixture as metal, setting an elastic modulus, a Poisson's ratio and a density, and conducting description by using an isotropic linear elastic constitutive model; and setting a bottom end of the fixture as a fixed end, constraining all freedom degrees, and meanwhile applying symmetry constraints in X and Y directions to two symmetry planes respectively; setting friction contact on upper and lower surfaces of the specimen, and setting a friction coefficient, and using a pressure loading mode, applying pressure to the lower surface of the specimen at a constant speed according to experimental pressure, and obtaining the modeled bulge data, wherein the modeled bulge data comprises a deformation and strain cloud diagram, a pressure-displacement curve, a damage distribution cloud diagram and local thinning data.
7. 7 The hydraulic bulge testing method for material properties of TTDPE according to claim 1, wherein the comparing the modeled tensile data and the tensile experiment data, and obtaining a mechanical response relation of the specimen specifically comprises: analyzing a tension deformation law of the specimen according to a load-displacement curve and equivalent strain cloud diagrams for different loading displacement; determining a necking change of the specimen according to a failure mechanism and a failure position; and determining an evolution law of the specimen from tension to fracture according to the necking change and a port shape.
8. 8. The hydraulic bulge testing method for material properties of HDPE according to claim 6, wherein the comparing the modeled bulge data and the bulge experiment data, and obtaining a mechanical response relation of the specimen specifically comprises: analyzing a specimen bulge deformation law according to the deformation and strain cloud diagram and the pressure-displacement curve obtained through modeling and an experiment; predicting a fracture position of the specimen according to the damage distribution cloud diagram; and analyzing a specimen thinning law according to the local thinning data.
9. 9. A hydraulic bulge testing system for material properties of HDPE, comprising: an experiment element configured to test material properties of a specimen through a uniaxial tensile test and a hydraulic bulge test, and obtain tensile experiment data and bulge experiment data; a modeling element configured to conduct finite element modeling according to the tensile experiment data and the bulge experiment data, and obtain modeled tensile data and modeled bulge data; and an analysis element configured to compare the modeled tensile data and the tensile experiment data, compare the modeled bulge data and the bulge experiment data, and obtain a mechanical response relation of the specimen.
10. 10. The hydraulic bulge testing system for material properties of HDPE according to claim 9, wherein the modeling element comprises a tensile modeling module and a bulge modeling module; the tensile modeling module is configured to: create a tensile finite element model for a specimen subjected to uniaxial tension conduct grid division on the tensile finite element model by using a three-dimensional eight-node reduced integration element; and use an explicit scheme integral ABAQUS/Explicit, set a density and a total mass scaling value, control loading displacement and a loading rate to be consistent with those in the uniaxial tensile test, conduct a modeling experiment, and obtain the modeled tensile data, wherein the modeled tensile data comprises a load-displacement curve, equivalent strain cloud diagrams for different loading displacement, a failure mechanism, a failure position and a port shape; and the bulge modeling module is configured to: create a hydraulic bulge finite element model according to a hydraulic bulge experiment device; conduct grid division on the hydraulic bulge finite element model by using a three-dimensional eight-node reduced integration element; set a hourglass control stiffness parameter in a first-order reduced integration element, so as to obtain a refined grid; use an explicit scheme integral ABAQUS/Explicit, setting a total mass scaling value, setting a fixture as metal, setting an elastic modulus, a Poisson's ratio and a density, and conducting description by using an isotropic linear elastic constitutive model; and set a bottom end of the fixture as a fixed end, constrain all freedom degrees, and meanwhile apply symmetry constraints in X and Y directions to two symmetry planes respectively; set friction contact on upper and lower surfaces of the specimen, and set a friction coefficient; and use a pressure loading mode, apply pressure to the lower surface of the specimen at a constant speed according to experimental pressure, and obtain the modeled bulge data, wherein the modeled bulge data comprises a deformation and strain cloud diagram, a pressure-displacement curve, a damage distribution cloud diagram and local thinning data.