INVESTIGATION OF THE INFLUENCE OF STRUCTURAL INHOMOGENEITIES ON THE STRENGTH OF WELDED JOINTS OF FUNCTIONALLY GRADIENT MATERIALS

А.В. Усов, Ю.O. Морозов, М.В. Куніцин, А.М. Тонконоженко, І.О. Черниш. Дослідження впливу структурних неоднорідностей на міцність зварних з’єднань функціонально-градієнтних матеріалів. Розглядається вплив дефектів на механічні властивості з’єднань функціонально-градієнтних матеріалів, який залежить від їх форми, умов експлуатації, та характеру навантаження. Наявність дефектів у зварних з’єднаннях суттєво знижують робочу здатність конструкцій, а при певних умовах можуть привести до їх руйнування. Проблема міцності конструкцій, які мають зварні з’єднання пов’язана з встановленням локальних концентраторів напружень біля дефектів типу тріщин, в яких напруження значно перевищують середні значення. Для визначення міцності зварних з’єднань і встановлення вимог які пред’являються до їх якості побудована математична модель, яка дозволяє досліджувати вплив найбільш вірогідних дефектів на міцність з’єднань. Врахування дефектності, що мають місце у зварювальних з’єднаннях на несучу здатність конструкцій можна реалізувати основним критерієм локального руйнування К1с та дією експлуатаційних навантажень. По знайденому із моделі значенню коефіцієнта інтенсивності напружень та величині теплового потоку, що діє на конструкцію і завдяки якому у з’єднанні формуються напруження, можна визначити граничні значення розміру дефекту, при якому цей дефект залишиться у стані рівноваги без формування із нього магістральної тріщини. Адекватність одержаних теоретичним шляхом результатів досліджень перевірялась на міцності зварних з’єднань алюмінієвих сплавів з урахуванням наявності в них гарячих тріщин. Деформаційне зміцнення зварних з’єднань, яке відбувається у високоміцних складних легованих алюмінієвих сплавів сприяє пониженню їх міцності в зв’язку з появою у них інтерметалідних фаз, а також не проварів. Ключові слова: міцність зварного з’єднання, дефектність, математична модель, коефіцієнт інтенсивності напружень, адекватність


Introduction
Various technological operations contribute to the occurrence of hereditary defects in the surface layer of products. These defects, being stress concentrators, contribute to crack formation, and, to the loss of the bearing capacity of structural elements both during their manufacturing and during operation.
Especially significant losses in the national economy from marriage because of hereditary defects that form in products during their manufacture and the operation of these products.
Reducing defects in the manufacture of structural elements, improving the operational properties of such products, is an important national economic task, the solution of which leads to significant savings in material resources, labor and cost of them, and improving reliability during their operation.

Analysis of recent research and publications
The effect of defects on the mechanical properties of welded joints [1 -6] of functionally gradient materials is determined by the size and shape of the defects, their repetition rate, construction material, operating conditions and nature of the load [7,8], therefore, the presence of defects in welded joints does not mean the loss of their performance. However, defects can significantly reduce the performance of structures and, under certain conditions, lead to their destruction. Therefore, to determine the reliability of welded structures and establish requirements for the quality of welded joints, it is necessary to have information about the influence of the most probable defects on the strength of joints. The greatest danger to structures is represented by internal defects since they must be detected without destroying the welded joint.
In structures operating under static and dynamic loads, the same defects unequally affect welded joints. Under a static load, the relative strength of the defect has the main effect on the strength of structures operating at temperatures down to -60 °C, provided that the material of the welded joint has a large plasticity margin. At lower temperatures, the strength is characterized by the intensity of the stresses in the defect zone. Under dynamic loads, the strength of welded joints is determined by their resistance to fatigue stresses [9,10]. Undercuts, pores, slag inclusions, and lack of penetration (and/or lack of fusion) reduce the durability of structures, being the causes of the formation of stress concentration. Cracks of any size are not allowed in welded joints, as they contribute to the concentration of internal stresses, quickly spreading deep into the metal.
Lack of penetration (and/or lack of fusion) has a significant effect on the impact strength of the weld metal. According to [7], a lack of penetration (and/or lack of fusion) of 10 % of the thickness of a welded joint can reduce fatigue strength by half, and a lack of penetration (and/or lack of fusion) of 40…50 % reduces the endurance limits of steel by 2.5 times.
The operation of welded structures shows that welding stresses and strains contribute to a decrease in the bearing capacity of structures [9]. Sometimes, changing the size and shape of the welded structure reduces its performance, spoils the appearance, and can even lead to destruction. There is a general pattern of reduction in the strength of welded structures under the influence of shock in the presence of undercuts, pores, slag inclusions, and lack of penetration. The types, quantity, and sizes of permissible internal defects depend on the design purpose.

The purpose of research
To build a mathematical model that allows us to study the effect of defects in welded joints on the strength of welded structures and to determine the requirements for their quality, and to verify its adequacy by the experimental method.

Statement of the main material
Consider an infinite composite cylindrical body ( Fig. 1) comprising three thin-walled transversally isotropic hollow cylinders, one of which is finite, 2h high, models a weld. Between the cylinders, the full adhesion conditions are satisfied, and inside the weld, there are flat defects of an arbitrary nature (such as cracks, delaminated, and not delaminated inclusions) [11 -17].
To determine the stress intensity factor under tensile load, it is necessary to construct a discontinuous solution [14] for a piecewise-homogeneous transversely isotropic space. Consider a space consisting of two different transversally isotropic half-spaces fully linked along the plane. On an arbitrary piecewise continuous surface Ω , defects of an arbitrary nature are located (such as cracks, exfoliated and non-exfoliated inclusions).
Stress and displacement components: .  To write the conditions on the surface Ω, where discontinuities of all components of the vectors σ and u are possible, we introduce at each point on the surface Ω the local coordinate systems (N, M, S) Fig. 1 b. To do this, draw a tangent plane P and a normal vector n to it at each point on the surface. The direction of the N axis coincides with the direction of the n vector. We choose the other two axes M, S mutually perpendicular to the plane P so that after the rotation of the axes, the directions of the axes (N, M, S) coincide with the direction of the corresponding axes (Z, X, Y). In the new coordinate system of stress and displacement, we denote this:  6  1  1  2  3  1  2  3  1  2  3   6  1  3  1  2  3  5  1  2  3  6  1  2  3  1  1  2  3  2  1  2  3  3  1  2  3   1  2  3   { } ,  , ,  , , , ( , , ) , , , , , , , , , , , , }, Point ( , , ) x y z + + + on the normal side n, and point ( , , ) x y z − − − is on the opposite side. For definiteness, on the surface Ω we assume the following jumps to be known: The solution of the boundary value problem (2), (3), (5), (6) must be sought in the class  1 ( ) L  is the space of functions integrable in 3  . We introduce the notation: Then equations (2), (3) can be represented as: We continue the matrix equation (7) to the entire space. To do this, using the properties of the generalized functions of slow growth , we continue the desired functions to the space 3 ( ) ′  I whose singularity carrier comprises the surface Ω, i.e., suppsing = Ω.
Given the relationship between conventional and generalized 1, , are the differentiation operators in the space δ Ω is the generalized Dirac function concentrated on the surface Ω. Taking into account formulas (8), we reduce the boundaryvalue problem (5), (6), (7) to the following boundary-value problem in the space vector system is called the fundamental solutions of a discontinuous (FSD) for a piecewise homogeneous transversely isotropic space if they satisfy the following system of boundary value problems: 9 1,9 [ , , , ] ; 1, 9, ( , , ) , , 3, 5, 9, ( ), If the fundamental solution is found, then the discontinuous solution is obtained using convolution: Applying the three-dimensional Fourier transform to (11), we obtain with respect to We will carry out all further calculations for the case when the surface Ω is a plane defect parallel to the plane 3 0 x = , i.e., when 1 2 0 κ =κ = and 3 1 κ =, therefore 0 , respectively. Using the theorems from [1] we obtain the representation: where 0 Then, taking into account (14)   To solve equations (15), we introduce the following combinations: where , are new unknown functions.
Let a disc-shaped elliptic crack z h = be contained in a composite transversely isotropic space in ( Given that 0 2 0 2  0  0  1  1  2  2  1  1  2  2  2  2  2  2  1  2  12  5  3  5  3  5  3  0 0 And introducing the following operators: we get: Unknown functions are presented in the form: where 0 0 1 2 ( , ) Z x x is a geometric description of the ∂Ω crack boundary. With an elliptical region rotated through the angle α , the function 0 0 1 2 ( , ) Z x x can be defined:  We obtain the expression for the stress intensity factor [18,19,20,21] depending on the geometric parameters of the defect and the applied load.
Where the crack contour is described by a second-order curve A B C D are the coefficients characterizing the shape of the curve (with an elliptical crack: , 0  2  2  0  3  2,5  1,7  6  12  9 2, 2 1 1, 4 2 0 0 0 From the found value of the stress intensity factor 0 1 ( ) k x and the value of the tensile stresses acting on the structure that forms the stresses 33 ( ) x σ , one can determine the limiting value of the size of the major semi-axis of the elliptical defect a , at which this defect remains in equilibrium without the formation of the main crack from it.
Results and Discussion. The adequacy of the results obtained theoretically by determining the intensity of stresses in places of accumulation of inhomogeneities will be checked on the strength of welded joints of aluminum alloys [9], taking into account the occurrence of hot cracks in them. A comparative analysis of softening and the strength level of welded joints of plastic low-alloyed aluminum alloys and high-strength complex-alloyed aluminum alloys are carried out. The strain hardening of the joints of high-strength complex alloyed aluminum alloys obtained during argon-arc welding with a non-consumable electrode (AWNCE) provides a higher level of their strength than in fusion welding. In structures of critical use, exposed to significant force impact, high-strength complex alloyed aluminum alloys are used. For experimental studies, plastic low-alloyed aluminum alloys AMtsN, AMg2M, and AMg5M were used, and high-strength complex alloyed aluminum alloys AMg6M, 1420, 1201 and 1460. The mechanical properties of the welded sheets 1.8 mm thick are given in Table. 1. Table 1 Mechanical properties of sheets of aluminum alloys with a thickness of 1.8 mm [7] Alloy grade σ v , MPa σ 0.2 , MPa δ, % α, degrees ISO EN GOST AlMn1 EN AW-3003 AMtsN  218  178  6  180  AIMg2  AIMg2  AMg2M  176  88  23  180  --AMg5M  332  160  22  142  5056  -AMg6M  359  210  22  96  --1420  459  322  11  50  2219  -1201  423  303  12  60  --1460  565  523  9  36 AWNCE was performed at a speed of 20 m/h on an MW450 installation (Fronius, Austria) using the filler materials (Table 2). Standard samples were used from the welded joints obtained to determine the uniaxial tensile strength. The tests were carried out using the universal multi-purpose servohydraulic system MTS 810. The samples obtained by AWNCE were tested after removing the weld melt flush with the base metal, and with additionally cleaned their reinforcements, since these and other types of joints are used in welded structures. The softening of the metal in the welding zone was tested by measuring its hardness on a ROCKWELL device at a load of 600 N and a ball diameter of 1/16″. For welded joints of plastic alloys AMtsN and AMg2M, the microhardness of the metal was measured using a PMT-3 microhardness tester with a load of 0.1 N. The microstructure of the welded joints was studied using a MIM-8M optical microscope. Cross-sections of the compounds obtained by AWNCE were preliminarily prepared by electrolytic polishing and their additional etching in a solution of perchloric, nitric, and hydrofluoric acids.
The conducted experimental studies made it possible to test softening, strength level, and structural features of the joints obtained by fusion welding. It was established that during AWNCE of plastic lowalloyed aluminum alloys AMtsN and AMg2M, the minimum hardness occurs in the metal, where the samples undergo tensile fracture, and in welded joints of the AMg5M alloy the minimum hardness is in the central part of the weld. Therefore, samples without reinforcement are destroyed along the seam, and with amplification, they are destroyed along the heataffected zone (HAZ).
It should be noted that the minimum values of metal hardness in the fracture zone of samples of welded joints of alloys AMtsN and AMg2M obtained by both welding methods are approximately the same, their tensile strength is at the level of 113 and 170 MPa, respectively (Table 3). Only samples without reinforcement from AMg5M alloy obtained by AWNCE have lower (300 MPa) strength and are destroyed in the central part of the weld, where the metal is characterized by minimal hardness. Therefore, structural changes in the weld metal and its fusion zones (FZ) with the base metal occurring during fusion welding of these alloys. practically do not affect the strength of welded seams.
So, when welding in the solid phase of the AMg6M alloy, the formation of fine grains in the weld leads to its strain hardening. Therefore, the destruction of such samples occurs according to the HAZ, where the metal hardness is minimal, and the strength is at the level of 336 MPa.
Non-reinforced Samples obtained by the AWNCE method break down along the seam and have a tensile strength of 324 MPa. The maximum strength (345 MPa) is characterized by reinforced specimens, which are destroyed by tension along the welded joint of the base metal.
In thermally hardened alloys (1420, 1201, and 1460), the solid solution is in a supersaturated state. Therefore, because of thermomechanical action in the welds, besides grinding the grains, there is a softening of the metal, because of the release of excess intermetallic phases from the solid solution and their coagulation. Small hardening phases in the weld core are partially dissolved, and large lowmelting intermetallic inclusions are partially melted, forming a new solid solution. * The average values of the indicators according to the test results of three to five samples are given Table 2 Welding conditions for aluminum alloys [7]  In the welded seams of such alloys obtained by AWNCE, the minimum hardness of the metal is observed in the central part of the welds, where the samples are destroyed without reinforcement [7]. Here, the difference in strength substantially depends on the chemical composition of the alloy being welded. So, if for alloy 1420 it is only 22 MPa, then for alloys 1460 and 1201, respectively, 52 and 71 MPa. This is because of the peculiarities of the formation of seams with AWNCE.
The formation of a compound in the solid phase because of the movement of plasticized metal in a limited volume at an over-pressure contributes to grain refinement, an increase in the volume fraction of boundaries and crushing of intermetallic phases.
The samples with reinforcement obtained by AWNCE are always destroyed along the weld zone of the base metal and have higher strength than the samples without reinforcement, which are destroyed by the weld metal.
Strain hardening of seams occurring in high-strength complex alloyed aluminum alloys AMg6M, 1420, 1201 and 1460 obtained by AWNCE helps to reduce their strength.
Grinding of grains, an increase in the volume fraction of their boundaries and crushing of intermetallic phases in the joints at AWNCE. Aluminum alloys help to reduce their softening.
Conclusions As a result of the research, methods for solving the scientific and technical problem are proposed, which consist in establishing design dependencies for determining the influence of hereditary defects formed in welded joints of structures on their crack resistance and creating technological requirements for the welding operation, taking into account accumulated damage and heterogeneities. The following tasks were solved: 1. The mechanism of the formation and development of defects such as cracks in welding joints of functionally gradient materials under the influence of thermomechanical phenomena accompanying the manufacturing technology and operation of structural elements is studied.
2. Mathematical models have been developed that describe the mechanical processes in the weld of structural elements, taking into account heterogeneities that affect the formation of cracks, which helps to reduce the bearing capacity of such elements.
3. The adequacy of the constructed model was checked on high-strength complex alloyed aluminum alloys obtained by argon-arc welding with a non-consumable electrode.